Chapter 2 Absolute Value Function Standard Cubic Function Page

Ch.2 FunctionsandGraphs

2.1 BasicsofFunctionsandTheirGraphs

1 FindtheDomainandRangeofaRelation

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Givethedomainandrangeoftherelation.

1) {(10

,

–5),(–7

,

7),(–9

,

1),(–9

,

–7)}

A) domain={–9

,

–7

,

10};range={1

,

7

,

–5

,

–7} B) domain={1

,

7

,

–5

,

–7};range={–9

,

–7

,

10}

C) domain={–9

,

–7

,

10

,

–19};range={1

,

7

,

–5

,

–7} D) domain={–9

,

–7

,

10

,

9};range={1

,

7

,

–5

,

–7}

2) {(–3

,

4),(7

,

1),(–9

,

–8),(–9

,

–9)}

A) domain={–3

,

–9

,

7};range={4

,

–8

,

1

,

–9} B) domain={–3

,

–9

,

7

,

9};range={4

,

–8

,

1

,

–9}

C) domain={–3

,

–9

,

7

,

–19};range={4

,

–8

,

1

,

–9} D) domain={4

,

–8

,

1

,

–9};range={–3

,

–9

,

7}

3) {(–4

,

3),(–5

,

–1),(9

,

–8),(8

,

1)}

A) domain={–4

,

9

,

8

,

–5};range={3

,

–8

,

1

,

–1}

B) domain={3

,

–8

,

1

,

–1};range={–4

,

9

,

8

,

–5}

C) domain={–4

,

9

,

8

,

–5};range={3

,

–3

,

–8

,

1

,

–1}

D) domain={–4

,

9

,

8

,

–5};range={3

,

3

,

–8

,

1

,

–1}

4) {(–6

,

–7),(–6

,

7),(–1

,

1),(–4

,

–2),(–8

,

–5)}

A) domain={–4

,

–1

,

–8

,

–6};range={–2

,

1

,

–5

,

7

,

–7}

B) domain={–4

,

–4

,

–1

,

–8

,

–6};range={–2

,

1

,

–5

,

7

,

–7}

C) domain={–4

,

14

,

–1

,

–8

,

–6};range={–2

,

1

,

–5

,

7

,

–7}

D) domain={–2

,

1

,

–5

,

7

,

–7};range={–4

,

–4

,

–1

,

–8

,

–6}

5) {(–1

,

–3),(–1

,

–2),(–1

,

0),(3

,

2),(15

,

4)}

A) domain:{–1

,

3

,

–1

,

15};range:{–3

,

–2

,

0,2

,

4} B) domain:{–3

,

–2

,

2

,

4};range:{–1

,

3

,

–1

,

15}

C) domain:{–3

,

–2

,

0,2

,

4};range:{–1

,

3

,

–1

,

15} D) domain:{–1

,

3

,

–1

,

15};range:{–3

,

–2

,

2

,

4}

6) {(–6

,

–3),(–8

,

–1),(–4

,

–7),(8

,

2),(5

,

–4)}

A) domain={8

,

–4

,

–6

,

–8

,

5};range={2

,

–7

,

–3

,

–1

,

–4}

B) domain={2

,

–7

,

–3

,

–1

,

–4};range={8

,

–4

,

–6

,

–8

,

5}

C) domain={8

,

2

,

–4

,

–7

,

–6};range={–3

,

–8

,

–1

,

5

,

–4}

D) domain={–3

,

–8

,

–1

,

5

,

–4};range={8

,

2

,

–4

,

–7

,

–6}

7) {(–2

,

3),(–1

,

0),(0,–1),(1

,

0),(3

,

8)}

A) domain:{–2

,

–1

,

0,1

,

3};range:{3

,

0

,

–1

,

8} B) domain:{–2

,

–1

,

1

,

3};range:{3

,

0

,

–1

,

8}

C) domain:{3

,

0

,

–1

,

8};range:{–2

,

–1

,

0,1

,

3} D) domain:{3

,

0

,

–1

,

8};range:{–2

,

–1

,

1

,

3}

2 DetermineWhetheraRelationisaFunction

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Determinewhethertherelationisafunction.

1) {(–2

,

–9),(3

,

–5),(6

,

6),(8

,

1),(11

,

2)}

A) Function B) Notafunction

2) {(–6

,

–5),(–3

,

–7),(4

,

6),(4

,

8)}

A) Notafunction B) Function

Page1

3) {(–7

,

–8),(–7

,

–5),(2

,

2),(4

,

–8),(10

,

6)}

A) Notafunction B) Function

4) {(3

,

–9),(3

,

3),(4

,

9),(7

,

4),(10

,

7)}

A) Notafunction B) Function

5) {(–6

,

9),(–3

,

6),(2

,

2),(8

,

4)}

A) Function B) Notafunction

6) {(–8

,

–9),(–8

,

9),(1

,

3),(3

,

5),(10

,

–9)}

A) Notafunction B) Function

7) {(–7

,

2),(–3

,

–3),(1

,

8),(2

,

3)}

A) Function B) Notafunction

8) {(–6

,

1),(–3

,

–6),(4

,

–6),(4

,

–3)}

A) Notafunction B) Function

9) {(–4

,

–4),(–2

,

1),(–1

,

–7),(5

,

–9)}

A) Function B) Notafunction

10) {(1

,

5),(2

,

3),(5

,

–3),(7

,

–3),(11

,

7)}

A) Function B) Notafunction

3 DetermineWhetheranEquationRepresentsaFunction

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Determinewhethertheequationdefinesyasafunctionofx.

1) x+y=36

A) yisafunctionofxB)yisnotafunctionofx

2) 2x+3y=15

A) yisafunctionofxB)yisnotafunctionofx

3) x2+y=16

A) yisafunctionofxB)yisnotafunctionofx

4) x+y2=4

A) yisafunctionofxB)yisnotafunctionofx

5) x2+y2=9

A) yisafunctionofxB)yisnotafunctionofx

6) y2=5x

A) yisafunctionofxB)yisnotafunctionofx

7) x=y2

A) yisafunctionofxB)yisnotafunctionofx

8) y=x2

A) yisafunctionofxB)yisnotafunctionofx

Page2

9) y=–x–9

A) yisafunctionofxB)yisnotafunctionofx

10) y=6x+4

A) yisafunctionofxB)yisnotafunctionofx

11) x+y3=27

A) yisafunctionofxB)yisnotafunctionofx

12) xy+9y=1

A) yisafunctionofxB)yisnotafunctionofx

13) |x|–y=9

A) yisafunctionofxB)yisnotafunctionofx

4 EvaluateaFunction

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Evaluatethefunctionatthegivenvalueoftheindependentvariableandsimplify.

1) f(x)=–5x+1; f(–3)

A) 16 B) 12 C) 14 D) –4

2) f(x)=x2–3; f(x–4)

A) x2–8x+13 B) x2+16 C) x2–8x+16 D) x2–7

3) f(x)=3x2–3x–4; f(x–1)

A) 3x2–9x+2B)

–9x2+3x+2C)3x

2–9x–4D)3x

2–15x–4

4) g(x)=3x+1; g(x+1)

A) 3x+4B)3x

+1C)3x

–1D)

1

3x+1

5) h(x)=x–15 ;h(20)

A) 5 B) –35 C) 35 D) –5

6) f(x)=x+6;f(

–2)

A) 2 B) –2 C) 1.41 D) notarealnumber

7) f(x)=x2+6

x3–5x ;f(

–4)

A) –1

2B) –11

32 C) –22

69 D) –4

11

8) f(x)=x3+3

x2–5;f(5)

A) 32

5B) 128

25 C) 25

4D) 7

5

Page3

Solvetheproblem.

9) ThefunctionP(x)=0.35x–74modelstherelationshipbetweenthenumberofpretzelsxthatacertainvendor

sellsandtheprofitthevendormakes.FindP(1000),theprofitthevendormakesfromselling1000pretzels.

A) $276 B) $350 C) $424 D) $926

10) Thetotalcostindollarsforacertaincompanytoproducexemptyjarstobeusedbyajellyproducerisgivenby

thefunctionC(x)=0.8x+40,000.FindC(50,000),thecostofproducing50,000jars.

A) $80,000 B) $40,000 C) $40.80 D) $50,040

Page4

5 GraphFunctionsbyPlottingPoints

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Graphthegivenfunctionsonthesamerectangularcoordinatesystem.Describehowthegraphofgisrelatedtothe

graphoff.

1) f(x)=x,g(x)=x+4

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

A) gshiftsthegraphoffverticallyup4 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

B) gshiftsthegraphoffverticallydown4 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

C) gshiftsthegraphoffverticallydown4 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

D) gshiftsthegraphoffverticallyup4 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

Page5

2) f(x)=x,g(x)=x–2

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

A) gshiftsthegraphoffverticallydown2 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

B) gshiftsthegraphoffverticallydown2 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

C) gshiftsthegraphoffverticallyup2 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

D) gshiftsthegraphoffverticallyup2 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

Page6

3) f(x)=–2x,g(x)=–2x–3

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

A) gshiftsthegraphoffverticallydown3 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

B) gshiftsthegraphoffverticallydown3 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

C) gshiftsthegraphoffverticallyup3 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

D) gshiftsthegraphoffverticallyup3 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

Page7

4) f(x)=x2,g(x)=x2+1

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

A) gshiftsthegraphoffverticallyup1 unit

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

B) gshiftsthegraphoffverticallydown1 unit

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

C) gshiftsthegraphoffverticallydown1 unit

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

D) gshiftsthegraphoffverticallyup1 unit

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

Page8

5) f(x)=2x2,g(x)=2x2–3

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

A) gshiftsthegraphoffverticallydown3 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

B) gshiftsthegraphoffverticallydown3 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

C) gshiftsthegraphoffverticallyup3 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

D) gshiftsthegraphoffverticallyup3 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

Page9

6) f(x)=x

,

g(x)=x+4

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

A) gshiftsthegraphoffverticallyup4 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

B) gshiftsthegraphoffverticallydown4 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

C) gshiftsthegraphoffverticallydown4 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

D) gshiftsthegraphoffverticallyup4 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

Page10

7) f(x)=x

,

g(x)=x–4

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

A) gshiftsthegraphoffverticallydown4 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

B) gshiftsthegraphoffverticallyup4 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

C) gshiftsthegraphoffverticallydown4 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

D) gshiftsthegraphoffverticallyup4 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

Page11

8) f(x)=x3,g(x)=x3+2

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

A) gshiftsthegraphoffverticallyup2 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

B) gshiftsthegraphoffverticallydown2 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

C) gshiftsthegraphoffverticallyup2 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

D) gshiftsthegraphoffverticallydown2 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

Page12

9) f(x)=x,g(x)=x+4

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

A) gshiftsthegraphoffverticallyup4 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

B) gshiftsthegraphoffverticallydown4 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

C) gshiftsthegraphoffverticallydown4 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

D) gshiftsthegraphoffverticallyup4 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

Page13

10) f(x)=x,g(x)=x–2

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

A) gshiftsthegraphoffverticallydown2 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

B) gshiftsthegraphoffverticallyup2 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

C) gshiftsthegraphoffverticallydown2 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

D) gshiftsthegraphoffverticallyup2 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

Page14

11) f(x)=x,g(x)=x+1

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

A) gshiftsthegraphoff1unittotheleft

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

B) gshiftsthegraphoff1unittotheright

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

C) gshiftsthegraphoffverticallyup1 unit

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

D) gshiftsthegraphoffverticallydown1 unit

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

Page15

12) f(x)=x,g(x)=x–3

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

A) gshiftsthegraphoff3unitstotheright

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

B) gshiftsthegraphoff3unitstotheleft

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

C) gshiftsthegraphoffverticallyup3 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

D) gshiftsthegraphoffverticallydown3 units

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

Page16

6 UsetheVerticalLineTesttoIdentifyFunctions

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Usetheverticallinetesttodeterminewhetherornotthegraphisagraphinwhichyisafunctionofx.

1)

x

y

x

y

A) function B) notafunction

2)

x

y

x

y

A) function B) notafunction

3)

x

y

x

y

A) notafunction B) function

Page17

4)

x

y

x

y

A) notafunction B) function

5)

x

y

x

y

A) function B) notafunction

6)

x

y

x

y

A) notafunction B) function

Page18

7)

x

y

x

y

A) function B) notafunction

8)

x

y

x

y

A) function B) notafunction

9)

x

y

x

y

A) function B) notafunction

Page19

10)

x

y

x

y

A) function B) notafunction

11)

x

y

x

y

A) notafunction B) function

12)

x

y

x

y

A) function B) notafunction

Page20

13)

x

y

x

y

A) notafunction B) function

7 ObtainInformationAboutaFunctionfromItsGraph

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Usethegraphtofindtheindicatedfunctionvalue.

1) y=f(x).Findf(–3)

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

A) 0.4 B) –0.4 C) 1.6 D) –1.6

2) y=f(x).Findf(3).

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

A) 1.5 B) 3 C) 9 D) –3

Page21

3) y=f(x).Findf(–5)

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

A) 5 B) –5C)17D)2

4) y=f(x).Findf(5)

x

–5–4–3–2–1 12345

y

12

10

8

6

4

2

-2

-4

-6

-8

-10

-12

x

–5–4–3–2–1 12345

y

12

10

8

6

4

2

-2

-4

-6

-8

-10

-12

A) 11 B) 9 C) –11 D) 2

5) y=f(x).Findf(–5)

x

–5–4–3–2–1 12345

y

13

12

11

10

9

8

7

6

5

4

3

2

1

-1

x

–5–4–3–2–1 12345

y

13

12

11

10

9

8

7

6

5

4

3

2

1

-1

A) 0.5 B) 11 C) 4.5 D) 3.5

Page22

ThegraphbelowshowsthepercentageofstudentsenrolledintheCollegeofEngineeringatStateUniversity.Usethe

graphtoanswerthequestion.

6) Doesthegraphrepresentafunction?

A) yes B) no

7) Iffrepresentsthefunction,findf(1980).

A) approximately15% B) approximately17%

C) approximately11.5% D) approximately10%

8) Iff(x)=26%,whatyearisrepresentedbyx?

A) 1990 B) 1985 C) 1995 D) 1980

9) Betweenwhattwoyearsisthedifferenceinfunctionvaluesequalto5%?

A)

b

etween1980and1985 B)

b

etween1985and1990

C)

b

etween1970and1975 D)

b

etween1960and1965

Page23

8 IdentifytheDomainandRangeofaFunctionfromItsGraph

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Usethegraphtodeterminethefunctionʹsdomainandrange.

1)

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

A) domain:(–∞

,

∞)

range:(–∞,∞)

B) domain:(–∞

,

∞)

range:y=1

C) domain:x=1

2

range:(–∞,∞)

D) domain:x=1

2

range:y=1

2)

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

A) domain:(–∞

,

∞)

range:[–2,∞)

B) domain:[–5

,

∞)

range:[–2,∞)

C) domain:(–∞

,

∞)

range:(–∞,∞)

D) domain:(–∞

,

–5)or(–5

,

∞)

range:(–∞,–2)or(–2,∞)

Page24

3)

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

A) domain:(–∞

,

∞)

range:(–∞,2]

B) domain:(–∞

,

∞)

range:(–∞,∞)

C) domain:(–∞

,

–3]

range:(–∞,2]

D) domain:(–∞

,

–3)or(–3

,

∞)

range:(–∞,2)or(2,∞)

4)

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

A) domain:[0,∞)

range:[–1,∞)

B) domain:[0,∞)

range:(–∞,∞)

C) domain:(–∞

,

∞)

range:[–1,∞)

D) domain:[0,∞)

range:[0,∞)

Page25

5)

x

–10–8-6-4-2 2 4 6 8

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 8

y

10

8

6

4

2

-2

-4

-6

-8

-10

A) domain:(–∞

,

∞)

range:[0,5]

B) domain:(–∞

,

∞)

range:[2,5]

C) domain:[0,5]

range:(–∞,∞)

D) domain:[2

,

5]

range:(–∞,∞)

9 IdentifyInterceptsfromaFunctionʹsGraph.

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Identifytheintercepts.

1)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) (–2

,

0),(0,6) B) (2

,

0),(0,6) C) (–2

,

0),(0,–6) D) (–6

,

0),(0,6)

2)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) (1

,

0),(0,6) B) (–1

,

0),(0,6) C) (1

,

0),(0,–6) D) (–6

,

0),(0,6)

Page26

3)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) (1

,

0),(0,–5) B) (–1

,

0),(0,–5) C) (1

,

0),(0,5) D) (–5

,

0),(0,5)

4)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) (6

,

0),(–6

,

0),(0,4),(0,–4) B) (6

,

0),(–6

,

0)

C) (0,4),(0,–4) D) (4

,

0),(–4

,

0),(0,6),(0,–6)

5)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) (–2

,

0),(0,8) B) (–2

,

0),(0,–8) C) (2

,

0),(0,8) D) (–2

,

–2),(8

,

8)

Page27

6)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) (7

,

0),(–7

,

0),(0,–7) B) (7

,

0),(–7

,

0)

C) (0,–7) D) (7

,

0),(–7

,

0),(0,0)

2.2 MoreonFunctionsandTheirGraphs

1 IdentifyIntervalsonWhichaFunctionIncreases,Decreases,orisConstant

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Identifytheintervalswherethefunctionischangingasrequested.

1) Increasing

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

A) (–2,2) B) (–3,3) C) (–2,∞)D)(

–3,∞)

Page28

2) Constant

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

A) (–∞

,

–1)or(3,∞)B)(

–1

,

0) C) (3,∞)D)(

–∞

,

0)

3) Increasing

x

–10–8-6-4–2 2 4 6 810

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

–10–8-6-4–2 2 4 6 810

y

5

4

3

2

1

-1

-2

-3

-4

-5

A) (3,∞) B) (3,6) C) (–2,∞)D)(

–2,0)

4) Increasing

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

A) (–2,–1)or(3,∞)B)(

–1,∞)C)(

–2,1) D) (–1,3)

Page29

5) Increasing

x

-12 -6 6 12

y

8

4

-4

-8

x

-12 -6 6 12

y

8

4

-4

-8

A) (0,5) B) (1,6) C) (0,6) D) (1,5)

6) Increasing

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

A) (0,3) B) (–∞

,

0) C) (–∞

,

–1) D) (–1

,

0)

7) Decreasing

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

A) (–3,–2) B) (0,–2) C) (–∞

,

–3) D) (–∞

,

–2)

Page30

8) Decreasing

x

-12 -6 6 12

y

8

4

-4

-8

x

-12 -6 6 12

y

8

4

-4

-8

A) (5,12) B) (6,1) C) (5,1) D) (6,12)

9) Decreasing

x

–10–8-6-4–2 2 4 6 810

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

–10–8-6-4–2 2 4 6 810

y

5

4

3

2

1

-1

-2

-3

-4

-5

A) (–∞

,

3) B) (–∞

,

–2) C) (0,3) D) (0,–2)

10) Constant

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

A) (–1,1) B) (1,2) C) (–2,–1) D) (2,∞)

Page31

2 UseGraphstoLocateRelativeMaximaorMinima

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Thegraphofafunctionfisgiven.Usethegraphtoanswerthequestion.

1) Findthenumbers,ifany,atwhichfhasarelativemaximum.Whataretherelativemaxima?

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

A) fhasarelativemaximumatx=0;therelativemaximumis3

B) fhasarelativemaximumatx=–1 and1;therelativemaximumis0

C) fhasarelativemaximumatx=1;therelativemaximumis3

D) fhasnorelativemaximum

2) Findthenumbers,ifany,atwhichfhasarelativeminimum.Whataretherelativeminima?

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

A) fhasarelativeminimumatx=–3 and3;therelativeminimumis0

B) fhasarelativeminimumatx=0;therelativeminimumis3

C) fhasarelativeminimumatx=–3;therelativeminimumis0

D) fhasnorelativeminimum

Page32

Usethegraphofthegivenfunctiontofindanyrelativemaximaandrelativeminima.

3) f(x)=x3–3x2+1

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

A) maximum:(0,1);minimum:(2,–3) B) maximum:(0,1);minimum:none

C) maximum:none;minimum:(2,–3) D) nomaximumorminimum

4) f(x)=x3–12x+2

x

–5–4–3–2–1 12345

y

20

16

12

8

4

-4

-8

-12

-16

-20

x

–5–4–3–2–1 12345

y

20

16

12

8

4

-4

-8

-12

-16

-20

A) minimum:(2,–14);maximum:(–2,18)

B) maximum:(–2,18)and(0,0);minimum:(2,–14)

C) maximum:(2,–14);minimum:(–2,18)

D) nomaximumorminimum

3 IdentifyEvenorOddFunctionsandRecognizeTheirSymmetries

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Determinewhetherthegivenfunctioniseven,odd,orneither.

1) f(x)=x3–5x

A) Odd B) Even C) Neither

2) f(x)=4x2+x4

A) Even B) Odd C) Neither

3) f(x)=x3–x2

A) Neither B) Even C) Odd

Page33

4) f(x)=–5x5+x3

A) Odd B) Even C) Neither

5) f(x)=x3+x2+4

A) Neither B) Even C) Odd

Usepossiblesymmetrytodeterminewhetherthegraphisthegraphofanevenfunction,anoddfunction,orafunction

thatisneitherevennorodd.

6)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A) Even B) Odd C) Neither

7)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A) Neither B) Odd C) Even

8)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A) Odd B) Even C) Neither

Page34

4 UnderstandandUsePiecewiseFunctions

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Evaluatethepiecewisefunctionatthegivenvalueoftheindependentvariable.

1) f(x)=4x+3ifx<2

5x+2ifx≥2;f(3)

A) 17 B) 14 C) 18 D) 20

2) f(x)=x–2ifx>–1

–(x–2)ifx≤–1;f(–2)

A) 4 B) –4C)

–2D)17

3) g(x)=

x2+5

x+8ifx≠–8

x–1ifx=–8

;g(5)

A) 30

13 B) 4 C) 10

13 D) 5

4) h(x)=

x2–7

x+6ifx≠–6

x–2ifx=–6

;h(–6)

A) –8 B) undefined C) –4D)8

Graphthefunction.

5) f(x)=x+1ifx<1

3ifx≥1

x

-5 5

y

5

-5

x

-5 5

y

5

-5

A)

x

-5 5

y

5

-5

(1, 2)

(1, 3)

x

-5 5

y

5

-5

(1, 2)

(1, 3)

B)

x

-5 5

y

5

-5

(1, 3)

(1, 2)

x

-5 5

y

5

-5

(1, 3)

(1, 2)

Page35

C)

x

-5 5

y

5

-5

(-1, 3)

(-1, 2)

x

-5 5

y

5

-5

(-1, 3)

(-1, 2)

D)

x

-5 5

y

5

-5

(-1, 3)

(-1, 2)

x

-5 5

y

5

-5

(-1, 3)

(-1, 2)

Page36

6) f(x)=–x+3ifx<2

2x–3ifx≥2

x

-5 5

y

5

-5

x

-5 5

y

5

-5

A)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

B)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

C)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

D)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

Page37

7) f(x)=

x+4if–8≤x<3

–9ifx=3

–x+7ifx>3

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

(-8, –4)

(3, 7)

(3, –9)

(3, 4)

x

-10 -5 5 10

y

10

5

-5

-10

(-8, –4)

(3, 7)

(3, –9)

(3, 4)

B)

x

-10 -5 5 10

y

10

5

-5

-10

(-8, –4)

(3, 7)

(3, –9)

(3, 4)

x

-10 -5 5 10

y

10

5

-5

-10

(-8, –4)

(3, 7)

(3, –9)

(3, 4)

C)

x

-10 -5 5 10

y

10

5

-5

-10

(-8, –3)

(3, 8)

(3, –9)

(3, 4)

x

-10 -5 5 10

y

10

5

-5

-10

(-8, –3)

(3, 8)

(3, –9)

(3, 4)

D)

x

-10 -5 5 10

y

10

5

-5

-10

(-8, –3)

(3, 8)

(3, –9)

(3, 4)

x

-10 -5 5 10

y

10

5

-5

-10

(-8, –3)

(3, 8)

(3, –9)

(3, 4)

Page38

Basedonthegraph,findtherangeofy=f(x).

8) f(x)=–1

2xifx≠0

–7ifx=0

x

-10 -5 5

y

10

5

-5

-10

(0, –7)

x

-10 -5 5

y

10

5

-5

-10

(0, –7)

A) (–∞

,

0)or(0,∞)B)(

–∞

,

∞)

C) (–10,10) D) (–∞

,

0)or{0}or(0,∞)

9) f(x)=

4if–6≤x<–2

|x| if–2≤x<8

xif8≤x≤13

x

-10 -5 5 10 15

y

10

5

-5

-10

(-6, 4) (-2, 4)

(-2, 2)

(8, 8)

(8, 2.8)

(13, 3.6)

x

-10 -5 5 10 15

y

10

5

-5

-10

(-6, 4) (-2, 4)

(-2, 2)

(8, 8)

(8, 2.8)

(13, 3.6)

A) [0,8) B) [0,∞) C) [0,13] D) [0,8]

Solvetheproblem.

10) Supposeacarrentalcompanycharges$88 forthefirstdayand$38 foreachadditionalorpartialday.LetS(x)

representthecostofrentingacarforxdays.FindthevalueofS(4.5).

A) $240 B) $221 C) $259 D) $171

11) Supposealifeinsurancepolicycosts$16 forthefirstunitofcoverageandthen$4foreachadditionalunitof

coverage.LetC(x)bethecostforinsuranceofxunitsofcoverage.Whatwill10unitsofcoveragecost?

A) $52 B) $56 C) $40 D) $24

12) Asalespersongetsacommissionof$1400 forthefirst$10,000ofsales,andthen$700foreachadditional

$10,000orpartialofsales.LetS(x)representthecommissiononxdollarsofsales.Findthevalueof

S(65,000).

A) $5600 B) $5250 C) 5950 D) $4550

Page39

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

13) Agascompanyhasthefollowingrateschedulefornaturalgasusageinsingle –familyresidences:

Monthlyservicecharge $8.80

Perthermservicecharge

1st25therms $0.6686/therm

Over25therms $0.85870/therm

Whatisthechargeforusing25thermsinonemonth?

Whatisthechargeforusing45thermsinonemonth?

ConstructafunctionthatgivesthemonthlychargeCforxthermsofgas.

14) Anelectriccompanyhasthefollowingratescheduleforelectricityusageinsingle–familyresidences:

Monthlyservicecharge$4.93

Perkilowattservicecharge

1st300kilowatts $0.11589/kW

Over300kilowatts $0.13321/kW

Whatisthechargeforusing300kilowattsinonemonth?

Whatisthechargeforusing375kilowattsinonemonth?

ConstructafunctionthatgivesthemonthlychargeCforxkilowattsofelectricity.

15) OneInternetserviceproviderhasthefollowingratescheduleforhigh–speedInternetservice:

Monthlyservicecharge $18.00

1st50hoursofuse free

Next50hoursofuse $0.25/hour

Over100hoursofuse $1.00/hour

Whatisthechargefor50hoursofhigh–speedInternetuseinonemonth?

Whatisthechargefor75hoursofhigh–speedInternetuseinonemonth?

Whatisthechargefor135hoursofhigh–speedInternetuseinonemonth?

16) Thewindchillfactorrepresentstheequivalentairtemperatureatastandardwindspeedthatwouldproduce

thesameheatlossasthegiventemperatureandwindspeed.Oneformulaforcomputingtheequivalent

temperatureis

W(t)=

t

33–(10.45+10 v–v)(33–t)

22.04

33–1.5958(33–t)



if0≤v<1.79

if1.79≤v<20

ifv≥20

wherevrepresentsthewindspeed(inmeterspersecond)andtrepresentstheairtemperature(°C).Compute

thewindchillforanairtemperatureof15°Candawindspeedof12meterspersecond.(Roundtheanswerto

onedecimalplace.)

Page40

17) Acellularphoneplanhadthefollowingscheduleofcharges:

Basicservice,including100minutesofcalls $20.00permonth

2nd100minutesofcalls $0.075perminute

Additionalminutesofcalls $0.10perminute

Whatisthechargefor200minutesofcallsinonemonth?

Whatisthechargefor250minutesofcallsinonemonth?

ConstructafunctionthatrelatesthemonthlychargeCforxminutesofcalls.

5 FindandSimplifyaFunctionʹsDifferenceQuotient

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Findandsimplifythedifferencequotientf(x+h)–f(x)

h,h≠0forthegivenfunction.

1) f(x)=3x–7

A) 3 B) 3+–14

hC) 3+6(x–7)

hD) 0

2) f(x)=3x2

A) 3(2x+h) B) 6

h+x+3h C) 3(2x2+2xh+h2)

hD) 3

3) f(x)=9

A) 0 B) 1 C) 1+18

hD) 9

4) f(x)=1

5x

A) –1

5x(x+h) B) –1

x(x+h) C) 1

5x D) 0

5) f(x)=x2+8x–9

A) 2x+h+8B)

2x2+2x+2xh+h2+h–18

h

C) 2x+h–9D)1

2.3 LinearFunctionsandSlope

1 CalculateaLineʹsSlope

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Findtheslopeofthelinethatgoesthroughthegivenpoints.

1) (2

,

–3),(–7

,

8)

A) –11

9B) –9

11 C) –1D)

11

9

Page41

2) (–8

,

–9),(–8

,

–3)

A) Undefined B) 0 C) 3

4D) 3

8

3) (6

,

–1),(2

,

–1)

A) 0 B) Undefined C) –1

4D) 1

2

4) (7

,

–6),(–4

,

–18)

A) 12

11 B) 11

12 C) –8D)

–12

11

5) (5

,

–7),(–8

,

–2)

A) –5

13 B) –2C)

–13

5D) –1

2

6) (–1

,

7),(–8

,

7)

A) 0 B) 2 C) 1 D) 9

7) (–1,1)and(1

2,4)

A) 2 B) 10

3C) 1

2D) –1

2

8) ( 1

5,3)and(1

5,0)

A) Undefined B) 15

7C) –7

15 D) –15

7

2 WritethePoint–SlopeFormoftheEquationofaLine

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Usethegivenconditionstowriteanequationforthelineinpoint –slopeform.

1) Slope=3

,

passingthrough(5

,

8)

A) y–8=3(x–5) B) y+8=3(x+5) C) x–8=3(y–5) D) y=3x–7

2) Slope=3

,

passingthrough(–7

,

8)

A) y–8=3(x+7) B) y+8=3(x–7) C) x–8=3(y+7) D) y=3x+29

3) Slope=5

6,passingthrough(3,5)

A) y–5=5

6(x–3) B) y+5=5

6(x+3) C) x–5=5

6(y–3) D) y=5

6x+3

4) Passingthrough(7

,

3)and(5

,

2)

A) y–3=1

2(x–7)ory–2=1

2(x–5) B) y–3=1

2(x–5)ory–2=1

2(x–7)

C) y+3=1

2(x+7)ory+2=1

2(x+5) D) y–3=7(x+7)ory–2=5(x–3)

Page42

5) Passingthrough(–4

,

–4)and(–2

,

–7)

A) y+4=–3

2(x+4)ory+7=–3

2(x+2) B) y+4=–3

2(x+2)ory+7=–3

2(x+4)

C) y–4=–3

2(x–4)ory–7=–3

2(x–2) D) y+4=–3

2x–4ory+7=–3

2x+4

6) Passingthrough(1

,

–5)withx–intercept= –1

A) y+5=–5

2(x–1)ory=–5

2(x+1) B) y–5=–5

2(x+1)ory=–5

2(x+1)

C) y+5=–5

2(x–1)ory=–5

2(x–1) D) y–1=–5

2xory–5=–5

2(x+1)

3 WriteandGraphtheSlope–InterceptFormoftheEquationofaLine

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Usethegivenconditionstowriteanequationforthelineinslope –interceptform.

1) Slope=3

,

passingthrough(3

,

8)

A) y=3x–1B)y=3x+1C)y–8=3x–3D)y–8=x–3

2) Slope=2

,

passingthrough(–6

,

3)

A) y=2x+15 B) y=2x–15 C) y–3=2x+6D)y–3=x+6

3) Slope=4

5,passingthrough(2,7)

A) y=4

5x+27

5B) y=4

5x–27

5C) y=mx+27

5D) y=4

5x+2

4) Slope=4

7,y–intercept=2

A) f(x)=4

7x+2 B) f(x)=–4

7x–2 C) f(x)=4

7x–2 D) f(x)=7

4x+7

2

5) Passingthrough(5

,

3)and(4

,

6)

A) y=–3x+18 B) y=mx+18 C) y–3= – 3(x–5) D) y=3x+18

6) Passingthrough(1

,

–8)and(–7

,

8)

A) y=–2x–6B)y=mx–6C)y+8= – 2(x–1) D) y=2x–6

7) Passingthrough(–8

,

–3)and(–4

,

–8)

A) y=–5

4x–13 B) y=mx–13 C) y+3=–5

4(x+8) D) y=5

4x–13

Page43

Graphthelinewhoseequationisgiven.

8) y=2x+1

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

A)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

B)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

C)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

D)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

Page44

9) y=–3x–1

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

A)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

B)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

C)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

D)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

Page45

10) y=3

4x–3

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

A)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

B)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

C)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

D)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

Page46

11) y=–3

4x+1

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

A)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

B)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

C)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

D)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

Page47

4 GraphHorizontalorVerticalLines

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Graphtheequationintherectangularcoordinatesystem.

1) x=4

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

A)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

B)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

C)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

D)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

Page48

2) y=4

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

A)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

B)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

C)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

D)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

Page49

3) f(x)=–5

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

A)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

B)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

C)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

D)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

Page50

4) 5y=15

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

A)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

B)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

C)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

D)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

Page51

5) 2x=8

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

A)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

B)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

C)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

D)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

Page52

6) 3y=21

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page53

7) 8x+1=–23

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

5 RecognizeandUsetheGeneralFormofaLineʹsEquation

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Determinetheslopeandthey–interceptofthegraphoftheequation.

1) y–7=0

A) m=0;(0,7) B) m=7;(0,0)

C) m=1;(0,7) D) m=0;noy–intercept

2) x+y–11=0

A) m=–1;(0,11) B) m=1;(0,11) C) m=0;(0,11) D) m= –1;(0,–11)

Page54

3) 3x+y–11=0

A) m=–3;(0,11) B) m=–1

3;0,11

3C) m=3;(0,11) D) m=3

11 ;0,1

11

4) 6x–7y–42=0

A) m=6

7;(0,–6) B) m=–6

7;(0,6) C) m=7

6;(0,7) D) m=6;(0,42)

5) x+15y–1=0

A) m=–1

15 ;0,1

15 B) m=1;(0,1) C) m=1

15 ;0,1

15 D) m= –15;(0,15)

6) –x+3y–27=0

A) m=1

3;(0,9) B) m=–1

3;(0,9) C) m= –1;(0,27) D) m=3;(0,–27)

Graphtheequation.

7) 4x+5y–18=0

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

A)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

B)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

Page55

C)

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

D)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

8) 2x–3y+2=0

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

A)

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

B)

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

Page56

C)

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

D)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

9) 2x–5y+23=0

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

A)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

B)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

Page57

C)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

D)

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

10) –3y+2x+5=0

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

A)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

B)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

Page58

C)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

D)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

5

4

3

2

1

-1

-2

-3

-4

-5

Page59

6 UseInterceptstoGraphtheGeneralFormofaLineʹsEquation

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Graphthelinearfunctionbyplottingthex–andy–intercepts.

1) –1

2x+y–4=0

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) intercepts:(0,4),(–8

,

0)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B) intercepts:(0,4),(8

,

0)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C) intercepts:(0,4),(–4

,

0)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D) intercepts:(0,–8),(8

,

0)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page60

2) 1

3x+y–2=0

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) intercepts:(0,2),(6

,

0)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B) intercepts:(0,2),(–6

,

0)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C) intercepts:(0,2),(–2

,

0)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D) intercepts:(0,–6),(6

,

0)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page61

3) –3x–18y–18=0

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) intercepts:(0,–1),(–6

,

0)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B) intercepts:(0,–1),(6

,

0)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C) intercepts:(0,–6),(–1

,

0)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D) intercepts:(0,6),(1

,

0)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page62

4) 6x–12y–36=0

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) intercepts:(0,–3),(6

,

0)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B) intercepts:(0,–3),(–6

,

0)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C) intercepts:(0,6),(–3

,

0)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D) intercepts:(0,–6),(3

,

0)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page63

5) 0.3x+0.5y–1.5=0

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) intercepts:(0,3),(5

,

0)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B) intercepts:(0,–3),(–5

,

0)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C) intercepts:(0,3),(–5

,

0)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D) intercepts:(0,–3),(5

,

0)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page64

7 ModelDatawithLinearFunctionsandMakePredictions

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Solve.

1) Aschoolhasjustpurchasednewcomputerequipmentfor$23,000.00. Thegraphshowsthedepreciationofthe

equipmentover5years.Thepoint(0,23,000)representsthepurchasepriceandthepoint(5,0)representswhen

theequipmentwillbereplaced.Writealinearequationinslope–interceptformthatmodelsthevalueofthe

equipment,y,xyearsafterpurchase.Usethemodeltopredictthevalueoftheequipmentafter3years?

x

2.5 5

y

25000

22500

20000

17500

15000

12500

10000

7500

5000

2500

x

2.5 5

y

25000

22500

20000

17500

15000

12500

10000

7500

5000

2500

A) y=–4600x+23,000;

valueafter3yearsis$9200.00;

B) y=23,000x+5;

valueafter3yearsis$9200.00

C) y=4600x–23,000;

valueafter3yearsis$9200.00

D) y= – 23,000x+23,000;

valueafter3yearsis$–46,000.00

2) Theaveragevalueofacertaintypeofautomobilewas$15,600 in1995 anddepreciatedto$4080 in2000.Lety

betheaveragevalueoftheautomobileintheyearx,wherex=0represents1995.Writealinearequationthat

modelsthevalueoftheautomobileintermsoftheyearx.

A) y=–2304x+15,600 B) y= –2304x+4080

C) y=–2304x–7440 D) y=–1

2304 x–4080

3) Aninvestmentisworth$3595in1994.By1998 ithasgrownto$5095.Letybethevalueoftheinvestmentin

theyearx,wherex=0represents1994.Writealinearequationthatmodelsthevalueoftheinvestmentinthe

yearx.

A) y=375x+3595 B) y=1

375 x+3595 C) y= –375x+6595 D) y= –375x+3595

4) Afaucetisusedtoaddwatertoalargebottlethatalreadycontainedsomewater.Afterithasbeenfillingfor5

seconds,thegaugeonthebottleindicatesthatitcontains28ouncesofwater.Afterithasbeenfillingfor12

seconds,thegaugeindicatesthebottlecontains63ouncesofwater.Letybetheamountofwaterinthebottlex

secondsafterthefaucetwasturnedon.Writealinearequationthatmodelstheamountofwaterinthebottlein

termsofx.

A) y=5x+3B)y=1

5x+27 C) y= –5x+53 D) y=5x+51

5) Whenmakingatelephonecallusingacallingcard,acalllasting6 minutescost$1.70.Acalllasting13 minutes

cost$3.10.Letybethecostofmakingacalllastingxminutesusingacallingcard.Writealinearequationthat

modelsthecostofamakingacalllastingxminutes.

A) y=0.2x+0.5 B) y=5x–283

10 C) y= –0.2x+2.9 D) y=0.2x–9.9

Page65

6) Avendorhaslearnedthat,bypricingcarmelapples at$1.50

,

saleswillreach115 carmelapplesperday.

Raisingthepriceto$2.25willcausethesalestofallto85carmelapplesperday.Letybethenumberof

carmelapplesthevendorsellsatxdollarseach.Writealinearequationthatmodelsthenumberof

carmelapplessoldperdaywhenthepriceisxdollarseach.

A) y=–40x+175 B) y=–1

40 x+9197

80 C) y=40x+55 D) y= –40x–175

7) Theaveragevalueofacertaintypeofautomobilewas$15,180 in1994 anddepreciatedto$8520 in1999.Lety

betheaveragevalueoftheautomobileintheyearx,wherex=0represents1994.Writealinearequationthat

modelsthevalueoftheautomobileintermsoftheyearx.

A) y=–1332x+15,180 B) y= –1332x+8520

C) y=–1332x+1860 D) y=–1

1332 x–8520

8) Aninvestmentisworth$3852in1994.By1999 ithasgrownto$6552.Letybethevalueoftheinvestmentin

theyearx,wherex=0represents1994.Writealinearequationthatmodelsthevalueoftheinvestmentinthe

yearx.

A) y=540x+3852 B) y=1

540 x+3852 C) y= –540x+9252 D) y= –540x+3852

9) Whenmakingatelephonecallusingacallingcard,acalllasting5 minutescost$1.45.Acalllasting12 minutes

cost$2.85.Letybethecostofmakingacalllastingxminutesusingacallingcard.Writealinearequationthat

modelsthecostofmakingacalllastingxminutes.

A) y=0.2x+0.45 B) y=5x–471

20 C) y= –0.2x+2.45 D) y=0.2x–9.15

10) Avendorhaslearnedthat,bypricinghotdogs at$1.50

,

saleswillreach129 hotdogsperday.Raisingtheprice

to$2.00willcausethesalestofallto109hotdogsperday.Letybethenumberofhotdogsthevendorsellsat

xdollarseach.Writealinearequationthatmodelsthenumberofhotdogssoldperdaywhenthepriceisx

dollarseach.

A) y=–40x+189 B) y=–1

40 x+10317

80 C) y=40x+69 D) y= –40x–189

Page66

2.4 MoreonSlope

1 FindSlopesandEquationsofParallelandPerpendicularLines

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Findanequationforthelinewiththegivenproperties.

1) ThesolidlineLcontainsthepoint(–2

,

4)andisperpendiculartothedottedlinewhoseequationisy=2x. Give

theequationoflineLinslope–interceptform.

x

-5 5

y

5

-5

x

-5 5

y

5

-5

A) y=–1

2x+3B)y–4=–1

2(x+2) C) y=1

2x+3D)y–4=2(x+2)

2) ThesolidlineLcontainsthepoint(3

,

2)andisparalleltothedottedlinewhoseequationisy=2x. Givethe

equationforthelineLinslope–interceptform.

x

-5 5

y

5

-5

x

-5 5

y

5

-5

A) y=2x–4B)y=2x–1C)y–2=2(x–3) D) y=2x+b

Usethegivenconditionstowriteanequationforthelineintheindicatedform.

3) Passingthrough(4

,

5)andparalleltothelinewhoseequationisy=2x–6;

point–slopeform

A) y–5=2(x–4) B) y–4=2(x–5) C) y–5=x–4D)y=2x

4) Passingthrough(2

,

5)andperpendiculartothelinewhoseequationisy=2x+7;

point–slopeform

A) y–5=–1

2(x–2) B) y–5=1

2(x+2) C) y–2=1

2(x–5) D) y= – 2x–12

5) Passingthrough(3

,

5)andparalleltothelinewhoseequationisy= –2x+3 ;

point–slopeform

A) y–5=–2(x–3) B) y–3= –2(x–5) C) y–5=x–3D)y=2x

Page67

6) Passingthrough(3

,

–5)andparalleltothelinewhoseequationisy= –3x+4;

slope–interceptform

A) y=–3x+4B)y=3x–4C)y= – 3x–4D)y=–1

3x–4

3

7) Passingthrough(3,5)andperpendiculartothelinewhoseequationisy=1

7x+4;

slope–interceptform

A) y=–7x+26 B) y=7x–26 C) y= – 7x–26 D) y=–1

7x–26

7

8) Passingthrough(2,3)andparalleltothelinewhoseequationisy=–1

4x+2;

slope–interceptform

A) y=–1

4x+7

2B) y=1

4x–7

2C) y=–1

4x–7

2D) y= – 4x–14

9) Passingthrough(4

,

4)andparalleltothelinewhoseequationis5x+y–3=0;

slope–interceptform

A) y=–5x+24 B) y=5x–24 C) y= – 5x–24 D) y=–1

5x–24

5

10) Passingthrough(5

,

5)andperpendiculartothelinewhoseequationis–3x+y–9=0;

slope–interceptform

A) y=–1

3x+20

3B) y=1

3x–20

3C) y=–1

3x–20

3D) y= – 3x–20

2 InterpretSlopeasRateofChange

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Findtheslopethendescribewhatitmeansintermsoftherateofchangeofthedependentvariableperunitchangein

theindependentvariable.

1) Thelinearfunctionf(x)=2.4x+26representsthepercentageofpeople,f(x),whograduatedfromcollegex

yearsafter1998.

A) m=2.4;thepercentageofpeoplegraduatingfromcollegehasincreasedatarateof2.4%peryearafter

1998.

B) m=–2.4;thepercentageofpeoplegraduatingfromcollegehasdecreasedatarateof2.4%peryearafter

1998.

C) m=26;thepercentageofpeoplegraduatingfromcollegehasincreasedatarateof26%peryearafter

1998.

D) m=2.4;thepercentageofpeoplegraduatingfromcollegehasdecreasedatarateof2.4%peryearafter

1998.

Page68

2) Thelinearfunctionf(x)=–7.2x+33modelsthepercentageofpeople,f(x),whoeatatfastfoodrestaurantseach

weekxyearsafter1998.

A) m=–7.2;thepercentageofpeopleeatingatfastfoodrestaurantseachweekhasdecreasedatarateof

–7.2%peryearafter1998.

B) m=7.2;thepercentageofpeopleeatingatfastfoodrestaurantseachweekhasincreasedatarateof

–7.2%peryearafter1998.

C) m=33;thepercentageofpeopleeatingatfastfoodrestaurantseachweekhasincreasedatarateof–7.2%

peryearafter1998.

D) m=7.2;thepercentageofpeopleeatingatfastfoodrestaurantseachweekhasincreasedatarateof7.2%

peryearafter1998.

3 FindaFunctionʹsAverageRateofChange

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Findtheaveragerateofchangeofthefunctionfromx1tox2.

1) f(x)=2xfromx1=2tox2=8

A) 1

3B) 2 C) 7 D) –3

10

2) f(x)=–3x2–xfromx1=5tox2=6

A) –34 B) –2C)

1

2D) –1

6

3) f(x)=5x+7fromx1=–1tox2=0

A) 5 B) –28 C) 1

2D) –1

6

Solvetheproblem.

4) FromAprilthroughDecember2000,thestockpriceofQRSCompanyhadarollercoasterride.Thechartbelow

indicatesthepriceofthestockatthebeginningofeachmonthduringthatperiod.Findthemonthlyaverage

rateofchangeinpricebetweenJuneandSeptember.

Month Price

April(x=1) 115

May 107

June 87

July 101

August 96

September 112

October 92

November 86

December 66

A) $8.33permonth B) –$8.33 permonth C) $12.50 permonth D) –$12.50 permonth

Page69

5) Alongwithincomes,peopleʹscharitablecontributionshavesteadilyincreasedoverthepastfewyears.The

tablebelowshowstheaveragedeductionforcharitablecontributionsreportedonindividualincometax

returnsfortheperiod1993to1998.Findtheaverageannualincreasebetween1995and1997.

Year CharitableContributions

1993 $1830

1994 $2370

1995 $2470

1996 $2800

1997 $3090

1998 $3180

A) $310peryear B) $620 peryear C) $355 peryear D) $360 peryear

6) Adeepseadivingbellisbeingloweredataconstantrate.After9 minutes,thebellisatadepthof300 ft.After

50minutesthebellisatadepthof1300ft.Whatistheaveragerateofloweringperminute?Roundtothe

nearesthundredthisneeded.

A) 24.4ftperminute B) 0.04 ftperminute C) 20.0 ftperminute D) 26.0 ftperminute

2.5 TransformationsofFunctions

1 RecognizeGraphsofCommonFunctions

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Usetheshapeofthegraphtonamethefunction.

1)

x

y

x

y

A) Constantfunction B) Identityfunction

C) Absolutevaluefunction D) Standardcubicfunction

Page70

2)

x

y

x

y

A) Identityfunction B) Constantfunction

C) Absolutevaluefunction D) Squarerootfunction

3)

x

y

x

y

A) Standardquadraticfunction B) Constantfunction

C) Standardcubicfunction D) Squarerootfunction

4)

x

y

x

y

A) Standardcubicfunction B) Constantfunction

C) Standardquadraticfunction D) Squarerootfunction

Page71

5)

x

y

x

y

A) Squarerootfunction B) Constantfunction

C) Standardquadraticfunction D) Standardcubicfunction

6)

x

y

x

y

A) Absolutevaluefunction B) Constantfunction

C) Identityfunction D) Standardcubicfunction

Page72

2 UseVerticalShiftstoGraphFunctions

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Beginbygraphingthestandardquadraticfunctionf(x)=x2.Thenusetransformationsofthisgraphtographthegiven

function.

1) g(x)=x2–2

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page73

Beginbygraphingthestandardsquarerootfunctionf(x)=x.Thenusetransformationsofthisgraphtographthe

givenfunction.

2) g(x)=x–1

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page74

Beginbygraphingthestandardabsolutevaluefunctionf(x)=x .Thenusetransformationsofthisgraphtographthe

givenfunction.

3) g(x)=x+3

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page75

Beginbygraphingthestandardfunctionf(x)=x3Thenusetransformationsofthisgraphtographthegivenfunction.

4) g(x)=x3+2

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page76

Usethegraphofthefunctionf,plottedwithasolidline,tosketchthegraphofthegivenfunctiong.

5) g(x)=f(x)–1

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

y=f(x)

A)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

B)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

C)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

D)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

Page77

Beginbygraphingthestandardcuberootfunctionf(x)=3xThenusetransformationsofthisgraphtographthegiven

function.

6) g(x)=3x+2

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page78

3 UseHorizontalShiftstoGraphFunctions

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Beginbygraphingthestandardquadraticfunctionf(x)=x2.Thenusetransformationsofthisgraphtographthegiven

function.

1) h(x)=(x–2)2

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page79

Beginbygraphingthestandardsquarerootfunctionf(x)=x.Thenusetransformationsofthisgraphtographthe

givenfunction.

2) h(x)=x+2

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page80

Beginbygraphingthestandardabsolutevaluefunctionf(x)=x .Thenusetransformationsofthisgraphtographthe

givenfunction.

3) h(x)=x–5–5

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page81

Usethegraphofthefunctionf,plottedwithasolidline,tosketchthegraphofthegivenfunctiong.

4) g(x)=x–3

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page82

Beginbygraphingthestandardfunctionf(x)=x3Thenusetransformationsofthisgraphtographthegivenfunction.

5) h(x)=(x–2)3

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page83

Usethegraphofthefunctionf,plottedwithasolidline,tosketchthegraphofthegivenfunctiong.

6) g(x)=f(x+1)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

y=f(x)

A)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

B)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

C)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

D)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

Page84

4 UseReflectionstoGraphFunctions

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Beginbygraphingthestandardquadraticfunctionf(x)=x2.Thenusetransformationsofthisgraphtographthegiven

function.

1) h(x)=–(x+2)2

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page85

Beginbygraphingthestandardsquarerootfunctionf(x)=x.Thenusetransformationsofthisgraphtographthe

givenfunction.

2) g(x)=–x+4

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page86

3) g(x)=–x+5

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page87

Beginbygraphingthestandardabsolutevaluefunctionf(x)=x .Thenusetransformationsofthisgraphtographthe

givenfunction.

4) h(x)=–x+5

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page88

Beginbygraphingthestandardcubicfunctionf(x)=x3.Thenusetransformationsofthisgraphtographthegiven

function.

5) g(x)=–x3–3

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page89

Usethegraphofthefunctionf,plottedwithasolidline,tosketchthegraphofthegivenfunctiong.

6) g(x)=–f(x)–2

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

y=f(x)

A)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

B)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

C)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

D)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

Page90

5 UseVerticalStretchingandShrinkingtoGraphFunctions

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Beginbygraphingthestandardabsolutevaluefunctionf(x)=x.Thenusetransformationsofthisgraphtographthe

givenfunction.

1) h(x)=2x+2

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page91

Beginbygraphingthestandardcubicfunctionf(x)=x3.Thenusetransformationsofthisgraphtographthegiven

function.

2) g(x)=–1

3x3

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page92

3) g(x)=1

4x3

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page93

Beginbygraphingthestandardquadraticfunctionf(x)=x2.Thenusetransformationsofthisgraphtographthegiven

function.

4) g(x)=2x2

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page94

Beginbygraphingthesquarerootfunctionf(x)=xThenusetransformationsofthisgraphtographthegivenfunction.

5) g(x)=2x+4

x

–10–8-6-4-2 2 4 6 8

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 8

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page95

Usethegraphofy=f(x)tographthegivenfunctiong.

6) g(x)=1f(x)

x

-12-10 -8 -6 -4 -2 2 4 6 8 10 12

y

12

10

8

6

4

2

-2

-4

-6

-8

-10

-12

x

-12-10 -8 -6 -4 -2 2 4 6 8 10 12

y

12

10

8

6

4

2

-2

-4

-6

-8

-10

-12

A)

x

-12-10 -8 -6 -4 -2 2 4 6 8 10 12

y

14

12

10

8

6

4

2

-2

-4

-6

-8

-10

-12

-14

x

-12-10 -8 -6 -4 -2 2 4 6 8 10 12

y

14

12

10

8

6

4

2

-2

-4

-6

-8

-10

-12

-14

B)

x

-12-10 -8 -6 -4 -2 2 4 6 8 10 12

y

14

12

10

8

6

4

2

-2

-4

-6

-8

-10

-12

-14

x

-12-10 -8 -6 -4 -2 2 4 6 8 10 12

y

14

12

10

8

6

4

2

-2

-4

-6

-8

-10

-12

-14

C)

x

-12-10 -8 -6 -4 -2 2 4 6 8 10 12

y

14

12

10

8

6

4

2

-2

-4

-6

-8

-10

-12

-14

x

-12-10 -8 -6 -4 -2 2 4 6 8 10 12

y

14

12

10

8

6

4

2

-2

-4

-6

-8

-10

-12

-14

D)

x

-12-10 -8 -6 -4 -2 2 4 6 8 10 12

y

14

12

10

8

6

4

2

-2

-4

-6

-8

-10

-12

-14

x

-12-10 -8 -6 -4 -2 2 4 6 8 10 12

y

14

12

10

8

6

4

2

-2

-4

-6

-8

-10

-12

-14

Page96

6 UseHorizontalStretchingandShrinkingtoGraphFunctions

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Beginbygraphingthestandardquadraticfunctionf(x)=x2.Thenusetransformationsofthisgraphtographthegiven

function.

1) h(x)=(1

2x+2)

2

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page97

Beginbygraphingthestandardsquarerootfunctionf(x)=x.Thenusetransformationsofthisgraphtographthe

givenfunction.

2) g(x)=1

2x+4

x

-16 -8 8 16

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

-16 -8 8 16

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

-16 -8 8 16

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

-16 -8 8 16

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

-16 -8 8 16

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

-16 -8 8 16

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

-16 -8 8 16

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

-16 -8 8 16

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

-16 -8 8 16

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

-16 -8 8 16

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page98

Beginbygraphingthestandardabsolutevaluefunctionf(x)=x .Thenusetransformationsofthisgraphtographthe

givenfunction.

3) g(x)=24x

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page99

Beginbygraphingthestandardfunctionf(x)=x3Thenusetransformationsofthisgraphtographthegivenfunction.

4) h(x)=1

2(–2x)3

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page100

Usethegraphofthefunctionf,plottedwithasolidline,tosketchthegraphofthegivenfunctiong.

5) g(x)=1

4x+4

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page101

7 GraphFunctionsInvolvingaSequenceofTransformations

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Beginbygraphingthestandardquadraticfunctionf(x)=x2.Thenusetransformationsofthisgraphtographthegiven

function.

1) h(x)=(x–5)2+7

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page102

2) h(x)=–(x+7)2–2

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page103

3) g(x)=–1

3(x–5)2+3

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page104

Beginbygraphingthestandardsquarerootfunctionf(x)=x.Thenusetransformationsofthisgraphtographthe

givenfunction.

4) g(x)=–x+2–2

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page105

5) h(x)= –x+1–2

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page106

6) g(x)=x+4+4

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page107

Beginbygraphingthestandardabsolutevaluefunctionf(x)=x .Thenusetransformationsofthisgraphtographthe

givenfunction.

7) g(x)=1

3x+5–4

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page108

Beginbygraphingthestandardcubicfunctionf(x)=x3.Thenusetransformationsofthisgraphtographthegiven

function.

8) h(x)=(x–2)3+2

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page109

9) g(x)=–(x–4)3+3

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page110

10) h(x)=1

4x3+2

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page111

Usethegraphofthefunctionf,plottedwithasolidline,tosketchthegraphofthegivenfunctiong.

11) g(x)=f(x–1)–1

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

y=f(x)

A)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

B)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

C)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

D)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

Page112

12) g(x)=–f(x+2)+2

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

y=f(x)

A)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

B)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

C)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

D)

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

x

–6–5–4–3–2–1 123456

y

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

Page113

Beginbygraphingthecuberootfunctionf(x)=3xThenusetransformationsofthisgraphtographthegivenfunction.

13) g(x)=–3x+3

x

–10–8-6-4-2 2 4 6 8

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 8

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

B)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

C)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

D)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

Page114

2.6 CombinationsofFunctions;CompositeFunctions

1 FindtheDomainofaFunction

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Findthedomainofthefunction.

1) f(x)=2x+3

A) (–∞

,

∞)B)[

–3

,

∞)C)(

–∞

,

0)∪(0,∞)D)(0,∞)

2) f(x)=x2+4

A) (–∞

,

∞)B)[

–4

,

∞)C)(

–4

,

∞)D)(

–∞

,

–4)∪(–4

,

∞)

3) f(x)=x2

x2+12

A) (–∞

,

∞)B)(

–∞

,

–12)∪(–12

,

∞)

C) (–12

,

∞)D)(

–∞

,

0)∪(0

,

∞)

4) g(x)=2x

x2–9

A) (–∞

,

–3)∪(–3

,

3)∪(3

,

∞)B)(

–∞

,

0)∪(0

,

∞)

C) (9

,

∞)D)(

–∞

,

∞)

5) h(x)=x–3

x3–81x

A) (–∞

,

–9)∪(–9

,

0)∪(0,9)∪(9

,

∞)B)(

–∞

,

0)∪(0

,

∞)

C) (–∞

,

3)∪(3

,

∞)D)(

–∞

,

∞)

6) f(x)=6–x

A) (–∞

,

6] B) (–∞

,

6)∪(6

,

∞)C)(

–∞,6]D)(

–∞,6)∪(6,∞)

7) x

x–4

A) (4

,

∞)B)[4

,

∞)C)(

–∞

,

4)∪(4

,

∞)D)(

–∞

,

∞)

8) f(x)=1

x–7

A) (–∞

,

7)∪(7

,

∞)B)(

–∞

,

∞)C)(7

,

∞)D)(

–∞

,

0)∪(0

,

∞)

9) f(x)=–6x

x+8

A) (–∞

,

–8)∪(–8

,

∞)B)(

–∞

,

∞)C)(

–∞

,

0)∪(0

,

∞)D)(

–∞

,

–8)

10) f(x)=x–7

x–6

A) (–∞

,

6)∪(6

,

∞)B)(

–∞

,

∞)

C) (–∞

,

6)∪(6

,

7)∪(7

,

∞)D)(

–∞

,

7)∪(7

,

∞)

11) f(x)=1

x–6+4

x+2

A) (–∞

,

–2)∪(–2

,

6)∪(6

,

∞)B)(

–∞

,

∞)

C) (–∞

,

–2)∪(–2

,

∞)D)(

–∞

,

6)∪(6

,

∞)

Page115

2 CombineFunctionsUsingtheAlgebraofFunctions,SpecifyingDomains

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Givenfunctionsfandg,performtheindicatedoperations.

1) f(x)=5x–6

,

g(x)=7x–5

Findf–g.

A) –2x–1B)

–2x–11 C) 12x–11 D) 2x+1

2) f(x)=8x2–7x, g(x)=x2–5x–14

Findf

g.

A) 8x2–7x

x2–5x–14 B) 8x

x+1C) 8x–7

–5D) 8–x

14

3) f(x)=8–8x, g(x)=–4x+8

Findf+g.

A) –12x+16 B) –4x+8C)4x D)

–4x+16

4) f(x)=5x+2, g(x)=9x–25

Findfg.

A) ( 5x+2)( 9x–25)B)(3x–5)( 5x+2)

C) (5x+2)(9x–25) D) (5x+2)(3x–5)

5) f(x)=8x+5

,

g(x)=7x+1

Findfg.

A) 56x2+43x+5B)56x

2+36x+5C)15x

2+43x+6D)56x

2+5

Givenfunctionsfandg,determinethedomainoff+g.

6) f(x)=4x–4

,

g(x)=5x+6

A) (–∞

,

∞)B)(

–∞

,

0)or(0,∞) C) (0,∞)D)(

–∞

,

–4)or(–4

,

∞)

7) f(x)=3x+3, g(x)=5

x–3

A) (–∞

,

3)or(3

,

∞)B)(

–∞

,

∞) C) (0,∞)D)(

–∞

,

–5)or(–5

,

∞)

8) f(x)=3x+5, g(x)=4

x+8

A) (–∞

,

–8)or(–8

,

∞)B)(

–∞

,

∞) C) (0,∞)D)(

–∞

,

–4)or(–4

,

∞)

9) f(x)=2x

x–1, g(x)=4

x+2

A) (–∞

,

–2)or(–2

,

1)or(1

,

∞)B)(

–∞

,

∞)

C) (–∞

,

–1)or(–1

,

2)or(2

,

∞)D)(

–∞

,

–4)or(–4

,

–2)or(–2

,

∞)

10) f(x)=3x2+6,g(x)=2x3+5

A) (–∞

,

∞)B)(

–∞

,

0)or(0,∞)

C) (0,∞)D)(

–∞

,

–3)or(–3

,

–2)or(–2

,

∞)

Findthedomainoftheindicatedcombinedfunction.

11) Findthedomainof(f–g)(x)whenf(x)=9x–2 andg(x)=6x–3.

A) Domain:(–∞

,

∞) B) Domain:(–2

,

9) C) Domain:(–9

,

2) D) Domain:(–2

,

∞)

Page116

12) Findthedomainof(fg)(x)whenf(x)=8x+2andg(x)=7x–9.

A) Domain:9

7,∞B) Domain:[0,∞) C) Domain:(–∞

,

∞) D) Domain: –9

7,∞

13) Findthedomainoff

g(x)whenf(x)=6x2–8xandg(x)=x2–8x–5.

A) Domain:–∞,4–21 ∪4–21,4+21 ∪4+21,∞

B) Domain:(–∞

,

∞)

C) Domain:–∞,4–21 ∪4–21,∞

D) Domain:–∞,4–21 ∩4–21,4+21 ∩4–21,∞

14) Findthedomainof(f+g)(x)whenf(x)=8–6xandg(x)= –2x+2.

A) Domain:(–∞

,

∞) B) Domain:(–∞

,

2) C) Domain:(–6

,

∞) D) Domain:(–8

,

6)

Solvetheproblem.

15) Thefollowinggraphshowstheprivate,publicandtotalnationalschoolenrollmentforstudentsforselectyears

from1970through2000.

i) Howisthegraphfortotalschoolenrollment,T,determinedfromthegraphoftheprivateenrollment,r,

andthepublicenrollment,u?

ii) Duringwhich10–yearperioddidthetotalnumberofstudentsenrolledincreasetheleast?

iii) Duringwhich10–yearperioddidthetotalnumberofstudentsenrolledincreasethemost?

A) i) Tisthesumofrandu.

ii) 1970–1980

iii) 1990–2000

B) i) Tisthesumofrandu.

ii) 1990–2000

iii) 1970–1980

C) i) Tisthesumofrandu.

ii) 1970–1980

iii) 1980–1990

D) i) Tisthedifferenceofrandu.

ii) 1970–1980

iii) 1990–2000

16) Afirmisconsideringanewproduct.Theaccountingdepartmentestimatesthatthetotalcost,C(x),of

producingxunitswillbe

C(x)=100x+4760.

Thesalesdepartmentestimatesthattherevenue,R(x),fromsellingxunitswillbe

R(x)=110x,

butthatnomorethan646unitscanbesoldatthatprice.Findandinterpret(R–C)(646).

A) $1700profit,incomeexceedscost

Itisworthittodevelopproduct.

B) –$1700 loss,costexceedsincome

Itisnotworthittodevelopproduct.

C) $140,420profit,incomeexceedscost

Itisworthittodevelopproduct.

D) $1122 profit,incomeexceedscost

Itisworthittodevelopproduct.

Page117

17) Thefunctionf(t)=–0.15t2+0.51t+31.4modelstheU.S.populationinmillions,ages65andolder,wheret

representsyearsafter1990.Thefunctiong(t)=0.51t2+11.39t+108.1modelsthetotalyearlycostofMedicare

inbillionsofdollars,wheretrepresentsyearsafter1990.Whatdoesthefunctiong

frepresent?Findg

f(15).

A) Costperpersoninthousandsofdollars.$74.28 thousand

B) Costperpersoninthousandsofdollars.$0.18 thousand

C) Costperpersoninthousandsofdollars.$0.01 thousand

D) Costperpersoninthousandsofdollars.$6.90 thousand

3 FormCompositeFunctions

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Forthegivenfunctionsfandg,findtheindicatedcomposition.

1) f(x)=17x2–8x, g(x)=9x–9

(f∘g)(8)

A) 66,969 B) 9207 C) 57,762 D) 64,512

2) f(x)=x2–2x–5, g(x)=x2+2x–1

(f∘g)(–5)

A) 163 B) 955 C) 251 D) 867

3) f(x)=4x+7

,

g(x)=4x–1

(f∘g)(x)

A) 16x+3B)16x+11 C) 16x+6D)16x+27

4) f(x)=–2x+2

,

g(x)=3x+2

(g∘f)(x)

A) –6x+8B)

–6x+6C)6x+8D)

–6x–4

5) f(x)=7

x+8, g(x)=4

5x

(f∘g)(x)

A) 35x

4+40x B) 4x+32

35x C) 35x

4–40x D) 7x

4+40x

6) f(x)=x–8

6, g(x)=6x+8

(g∘f)(x)

A) x B) 6x+40 C) x+16 D) x–4

3

7) f(x)=4x2+3x+8, g(x)=3x–4

(g∘f)(x)

A) 12x2+9x+20 B) 12x2+9x+28 C) 4x2+9x+20 D) 4x2+3x+4

Page118

4 DetermineDomainsforCompositeFunctions

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Findthedomainofthecompositefunctionf∘g.

1) f(x)=4x+32

,

g(x)=x+7

A) (–∞

,

∞)B)(

–∞

,

–15)or(–15

,

∞)

C) (–∞

,

15)or(15

,

∞)D)(

–∞

,

–8)or(–8

,

–7)(–7

,

∞)

2) f(x)=10

x+7, g(x)=x+4

A) (–∞

,

–11)or(–11

,

∞)B)(

–∞

,

–7)or(–7

,

∞)

C) (–∞

,

–7)or(–7

,

–4)or(–4

,

∞)D)(

–∞

,

∞)

3) f(x)=x+1, g(x)=9

x+8

A) (–∞

,

–8)or(–8

,

∞)B)(

–∞

,

–9)or(–9

,

∞)

C) (–∞

,

–8)or(–8

,

–1)or(–1

,

∞)D)(

–∞

,

∞)

4) f(x)=2

x+4, g(x)=4

x

A) (–∞

,

–1)or(–1

,

0)or(0,∞)B)(

–∞

,

–4)or(–4

,

0)or(0,∞)

C) (–∞

,

–4)or(–4

,

–1)or(–1

,

0)or(0,∞)D)(

–∞

,

∞)

5) f(x)=x; g(x)=2x+12

A) [–6

,

∞) B) [0,∞)C)(

–∞

,

–6]or[0,∞)D)(

–∞

,

∞)

6) f(x)=3x+9; g(x)=x

A) [0,∞)B)[

–3

,

∞)C)(

–∞

,

–3]or[0,∞)D)(

–∞

,

∞)

5 WriteFunctionsasCompositions

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Findfunctionsfandgsothath(x)=(f∘g)(x).

1) h(x)=1

x2–9

A) f(x)=1/x,g(x)=x2–9 B) f(x)=1/9,g(x)=x2–9

C) f(x)=1/x2,g(x)=–1/9 D) f(x)=1/x2,g(x)=x–9

2) h(x)=|2x+3|

A) f(x)=|x|,g(x)=2x+3 B) f(x)= –|x|,g(x)=2x+3

C) f(x)=|–x|,g(x)=2x–3 D) f(x)=x,g(x)=2x+3

3) h(x)=1

x2+9

A) f(x)=x+9,g(x)=1/x2B) f(x)=1/x2,g(x)=9

C) f(x)=1/x,g(x)=1/x+9 D) f(x)=x,g(x)=1/x+9

Page119

4) h(x)=1

8x+10

A) f(x)=1/ x,g(x)=8x+10 B) f(x)=1

/

x,g(x)=8x+10

C) f(x)=8x+10,g(x)=1 D) f(x)=1,g(x)=8+10

5) h(x)=(4x–19)7

A) f(x)=x7,g(x)=4x–19 B) f(x)=4x–19,g(x)=x7

C) f(x)=(4x)7,g(x)=–19 D) f(x)=4x7,g(x)=x–19

6) h(x)=–36x2+10

A) f(x)=x,g(x)=–36x2+10 B) f(x)=–36x2+10,g(x)=x

C) f(x)=–36x+10,g(x)=x2D) f(x)=–36x2,g(x)=10

2.7 InverseFunctions

1 VerifyInverseFunctions

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Determinewhichtwofunctionsareinversesofeachother.

1) f(x)=4x g(x)=x

4h(x)=4

x

A) f(x)andg(x) B) f(x)andh(x) C) g(x)andh(x) D) None

2) f(x)=xg(x)=1

xh(x)=x2

A) f(x)andh(x) B) f(x)andg(x) C) g(x)andh(x) D) None

3) f(x)= x+6

4g(x)=4x+6 h(x)= x–6

4

A) g(x)andh(x) B) f(x)andg(x) C) f(x)andh(x) D) None

4) f(x)= x–6

4g(x)=4x–6 h(x)= x–4

–6

A) None B) f(x)andg(x) C) f(x)andh(x) D) g(x)andh(x)

5) f(x)=x4–6 g(x)=4x–6h(x)=x4+6

A) g(x)andh(x) B) f(x)andg(x) C) f(x)andh(x) D) None

2 FindtheInverseofaFunction

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Findtheinverseoftheone–to–onefunction.

1) f(x)=4x+8

A) f–1(x)=x–8

4B) f–1(x)=x+8

4C) f–1(x)=y–8

4D) f–1(x)=4x–8

4

Page120

2) f(x)=6x–7

5

A) f–1(x)=5x+7

6B) f–1(x)=5x–7

6C) f–1(x)=5

6x+7D) f–1(x)=5

6x–7

3) f(x)=3

7x–8

A) f–1(x)=3

7x +8

7B) f–1(x)=3

7y+8

7

C) f–1(x)=7x–8

3D) f–1(x)=–8

7– 3

7x

4) f(x)=(x–8)3

A) f–1(x)=3x+8B)f

–1(x)=3x–8C)f

–1(x)=x+8D)f

–1(x)=3x+512

5) f(x)=x+4

A) f–1(x)=x2–4B)f

–1(x)=1

x2–4C) f–1(x)=x–4D)f

–1(x)=x2+4

6) f(x)=3x–7

A) f–1(x)=x3+7B)f

–1(x)=1

x3+7C) f–1(x)=x+7D)f

–1(x)=x3+49

3 UsetheHorizontalLineTesttoDetermineifaFunctionhasanInverseFunction

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Doesthegraphrepresentafunctionthathasaninversefunction?

1)

x

y

x

y

A) Yes B) No

Page121

2)

x

y

x

y

A) No B) Yes

3)

x

y

x

y

A) Yes B) No

4)

x

y

x

y

A) No B) Yes

Page122

5)

x

y

x

y

A) No B) Yes

6)

x

y

x

y

A) Yes B) No

7)

x

y

x

y

A) Yes B) No

Page123

8)

x

y

x

y

A) No B) Yes

4 UsetheGraphofaOne–to–OneFunctiontoGraphItsInverseFunction

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Usethegraphofftodrawthegraphofitsinversefunction.

1)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page124

2)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

3)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page125

4)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page126

5)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page127

6)

x

-10 10

y

10

-10

x

-10 10

y

10

-10

A)

x

-10 10

y

10

-10

x

-10 10

y

10

-10

B)

x

-10 10

y

10

-10

x

-10 10

y

10

-10

C)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page128

5 FindtheInverseofaFunctionandGraphBothFunctionsontheSameAxes

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Graphfasasolidlineandf–1asadashedlineinthesamerectangularcoordinatespace.Useintervalnotationtogive

thedomainandrangeoffandf–1.

1) f(x)=2x–5

x

–10–8-6-4-2 2 4 6 8

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 8

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

f

domain=(–∞,∞);range=(–∞,∞)

f

–1domain=(–∞,∞);range=(–∞,∞)

B)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

f

domain=(–10,10);range=(–10,10)

f

–1domain=(–10,10);range=(–10,10)

Page129

C)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

f

domain=(–∞,∞);range=(–∞,∞)

f

–1domain=(–∞,∞);range=(–∞,∞)

D)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

f

domain=(–10,10);range=(–10,10)

f

–1domain=(–10,10);range=(–10,10)

2) f(x)=x2–6,x≥0

x

–10–8-6-4-2 2 4 6 8

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 8

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

f

domain=(0,∞);range=(–6,∞)

f

–1domain=(0,∞);range=(–6,∞)

B)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

f

domain=(–∞,∞);range=(–6,∞)

f

–1domain=(–∞,∞);range=(–6,∞)

Page130

C)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

f

domain=(0,∞);range=(–6,∞)

f

–1domain=(0,∞);range=(6,∞)

D)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

f

domain=(–∞,∞);range=(–6,∞)

f

–1domain=(–∞,∞);range=(6,∞)

3) f(x)=(x–4)2,x≥4

x

–10–8-6-4-2 2 4 6 8

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 8

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

f

domain=(4,∞);range=(0,∞)

f

–1domain=(0,∞);range=(4,∞)

B)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

f

domain=(–∞,∞);range=(0,∞)

f

–1domain=(0,∞);range=(–∞,∞)

Page131

C)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

f

domain=(–∞,∞);range=(0,∞)

f

–1domain=(0,∞);range=(–∞,∞)

D)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

Hasnoinverse

f

domain=(–∞,∞);range=(0,∞)

4) f(x)=x3–3

x

–10–8-6-4-2 2 4 6 8

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 8

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

f

domain=(–∞,∞);range=(–∞,∞)

f

–1domain=(–∞,∞);range=(–∞,∞)

B)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

f

domain=(–∞,∞);range=(–∞,∞)

f

–1domain=(–∞,∞);range=(–∞,∞)

Page132

C)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

f

domain=(–∞,∞);range=(–∞,∞)

f

–1domain=(–∞,∞);range=(–∞,∞)

D)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

f

domain=(0,∞);range=(–3,∞)

f

–1domain=(–3,∞);range=(0,∞)

5) f(x)=(x+3)3

x

–10–8-6-4-2 2 4 6 8

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 8

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

f

domain=(–∞,∞);range=(–∞,∞)

f

–1domain=(–∞,∞);range=(–∞,∞)

B)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

f

domain=(–∞,∞);range=(–∞,∞)

f

–1domain=(–∞,∞);range=(–∞,∞)

Page133

C)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

f

domain=(–∞,∞);range=(–∞,∞)

f

–1domain=(–∞,∞);range=(–∞,∞)

D)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

f

domain=(–∞,∞);range=(–∞,∞)

f

–1domain=(–∞,∞);range=(–∞,∞)

6) f(x)=x–4

x

–10–8-6-4-2 2 4 6 8

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 8

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

f

domain=(0,∞);range=(4,∞)

f

–1domain=(4,∞);range=(0,∞)

B)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

f

domain=(0,∞);range=(4,∞)

f

–1Hasnoinverse.

Page134

C)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

f

domain=(0,∞);range=(–4,∞)

f

–1domain=(–4,∞);range=(0,∞)

D)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

f

domain=(0,∞);range=(4,∞)

f

–1domain=(–4,∞);range=(0,∞)

7) f(x)=3x+5

x

–10–8-6-4-2 2 4 6 8

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 8

y

10

8

6

4

2

-2

-4

-6

-8

-10

A)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

f

domain=(–∞,∞);range=(–∞,∞)

f

–1domain=(–∞,∞);range=(–∞,∞)

B)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

f

domain=(–∞,∞);range=(0,∞)

f

–1domain=(0,∞);range=(–∞,∞)

Page135

C)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

f

domain=(–∞,∞);range=(–∞,∞)

f

–1domain=(–∞,∞);range=(–∞,∞)

D)

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 2468

y

10

8

6

4

2

-2

-4

-6

-8

-10

f

domain=(–∞,∞);range=(–∞,∞)

f

–1domain=(–∞,∞);range=(–∞,∞)

2.8 DistanceandMidpointFormulas;Circles

1 FindtheDistanceBetweenTwoPoints

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Findthedistancebetweenthepairofpoints.

1) (–2

,

–3)and(–14

,

2)

A) 13 B) 169 C) 14 D) 26

2) (2

,

6)and(–4

,

–7)

A) 205 B) 133 C) 78 D) –7

3) (3

,

–3)and(7

,

–1)

A) 2 5 B) 12 3 C) 12 D) 2

4) (–1

,

–6)and(6

,

–7)

A) 5 2 B) 48 3 C) 48 D) 8

5) (7

,

6)and(–7

,

–2)

A) 2 65 B) 132 33 C) 132 D) 6

6) (2 3,–3)and(6 3,1)

A) 8 B) 64 C) 7 D) 32

7) (0,0)and(–9

,

7)

A) 130 B) 130 C) –2D)4

8) (0,–1)and(–3

,

–1)

A) 3 B) 1 C) 10 D) 9

Page136

2 FindtheMidpointofaLineSegment

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Findthemidpointofthelinesegmentwhoseendpointsaregiven.

1) (7

,

5)and(5

,

3)

A) (6

,

4) B) (1

,

1) C) (2

,

2) D) (12

,

8)

2) (6

,

–6)and(–7

,

–3)

A) (–1

2,–9

2)B)(

13

2,–3

2)C)(13

,

–3) D) (–1

,

–9)

3) (2,–6

5)and(5

3,1)

A) ( 11

6,–1

10 )B)(

1

6,–11

10 )C)(

11

3,–1

5)D)(

–1

6,11

10 )

4) (–92

,47)and(–62,97)

A) ( –15 2

2,13 7

2)B)(

32

2,57

2)C)(

–32

2,–57

2)D)(

–15 2,13 7)

3 WritetheStandardFormofaCircleʹsEquation

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Writethestandardformoftheequationofthecirclewiththegivencenterandradius.

1) (–8

,

–9);5

A) (x+8)2+(y+9)2=25 B) (x–8)2+(y–9)2=25

C) (x+9)2+(y+8)2=5D)(x–9)2+(y–8)2=5

2) (7

,

0);7

A) (x–7)2+y2=49 B) (x+7)2+y2=49 C) x2+(y–7)2=7D)x

2+(y+7)2=7

3) (0,–4);7

A) x2+(y+4)2=49 B) x2+(y–4)2=7C)(x+4)2+y2=49 D) (x–4)2+y2=49

4) (1,8);14

A) (x–1)2+(y–8)2=14 B) (x+1)2+(y+8)2=14

C) (x–8)2+(y–1)2=196 D) (x+8)2+(y+1)2=196

5) (0,–6);15

A) x2+(y+6)2=15 B) x2+(y–6)2=15 C) (x+6)2+y2=225 D) (x–6)2+y2=225

6) (0,0);14

A) x2+y2=196 B) x2+y2=14 C) x2+y2=28 D) x2–y2=14

7) (0,0);14

A) x2+y2=14 B) x2+y2=14 C) x2+y2=7D)x

2+y2=196

Page137

4 GivetheCenterandRadiusofaCircleWhoseEquationisinStandardForm

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Findthecenterandtheradiusofthecircle.

1) (x+2)2+(y–3)2=49

A) (–2

,

3),r=7B)(3

,

–2),r=7C)(2

,

–3),r=49 D) (–3

,

2),r=49

Graphtheequationandstateitsdomainandrange.Useintervalnotation

2) x2+y2=36

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Domain=(–6,6);Range=(–6,6)

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Domain=(–6,6);Range=(–6,6)

Page138

Graphtheequation.

3) (x–1)2+(y–1)2=25

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Domain=(–4,6),Range=(–4,6)

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Domain=(–6,4),Range=(–6,4)

5 ConverttheGeneralFormofaCircleʹsEquationtoStandardForm

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Completethesquareandwritetheequationinstandardform.Thengivethecenterandradiusofthecircle.

1) x2–10x+25+y2+4y+4=4

A) (x–5)2+(y+2)2=4

(5,–2),r=2

B) (x+2)2+(y–5)2=4

(–2,5),r=2

C) (x–5)2+(y+2)2=4

(–5,2),r=4

D) (x+2)2+(y–5)2=4

(2,–5),r=4

2) x2+y2–18x+4y+85=9

A) (x–9)2+(y+2)2=9

(9,–2),r=3

B) (x+2)2+(y–9)2=9

(–2,9),r=3

C) (x–9)2+(y+2)2=9

(–9,2),r=9

D) (x+2)2+(y–9)2=9

(2,–9),r=9

3) x2+y2+10x+14y=–70

A) (x+5)2+(y+7)2=4

(–5,–7),r=2

B) (x+7)2+(y+5)2=4

(–7,–5),r=2

C) (x+5)2+(y+7)2=4

(5,7),r=4

D) (x+7)2+(y+5)2=4

(7,5),r=4

Page139

4) 6x2+6y2=36

A) x2+y2=6

(0,0),r=6

B) x2+y2=6

(0,0),r=6

C) x2+y2=36

(0,0),r=6

D) (x–6)2+(y–6)2=6

(6,6),r=6

5) x2+y2–12x+8y+40=0

A) (x–6)2+(y+4)2=12

(6,–4),r=23

B) (x–6)2+(y+4)2=12

(6,–4),r=12

C) (x–6)2+(y+4)2=12

(–6,4),r=23

D) (x+6)2+(y–4)2=12

(–6,4),r=23

Graphtheequation.

6) x2+y2–2x–10y+17=0

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page140

7) x2+y2+4x+4y–28=0

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page141

Ch.2 FunctionsandGraphs

AnswerKey

2.1 BasicsofFunctionsandTheirGraphs

1 FindtheDomainandRangeofaRelation

2 DetermineWhetheraRelationisaFunction

3 DetermineWhetheranEquationRepresentsaFunction

4 EvaluateaFunction

5 GraphFunctionsbyPlottingPoints

Page142

6 UsetheVerticalLineTesttoIdentifyFunctions

7 ObtainInformationAboutaFunctionfromItsGraph

8 IdentifytheDomainandRangeofaFunctionfromItsGraph

9 IdentifyInterceptsfromaFunctionʹsGraph.

2.2 MoreonFunctionsandTheirGraphs

1 IdentifyIntervalsonWhichaFunctionIncreases,Decreases,orisConstant

Page143

2 UseGraphstoLocateRelativeMaximaorMinima

3 IdentifyEvenorOddFunctionsandRecognizeTheirSymmetries

4 UnderstandandUsePiecewiseFunctions

5 FindandSimplifyaFunctionʹsDifferenceQuotient

Page144

2.3 LinearFunctionsandSlope

1 CalculateaLineʹsSlope

2 WritethePoint–SlopeFormoftheEquationofaLine

3 WriteandGraphtheSlope–InterceptFormoftheEquationofaLine

4 GraphHorizontalorVerticalLines

5 RecognizeandUsetheGeneralFormofaLineʹsEquation

6 UseInterceptstoGraphtheGeneralFormofaLineʹsEquation

Page145

7 ModelDatawithLinearFunctionsandMakePredictions

2.4 MoreonSlope

1 FindSlopesandEquationsofParallelandPerpendicularLines

2 InterpretSlopeasRateofChange

3 FindaFunctionʹsAverageRateofChange

6) A

2.5 TransformationsofFunctions

1 RecognizeGraphsofCommonFunctions

2 UseVerticalShiftstoGraphFunctions

3 UseHorizontalShiftstoGraphFunctions

4 UseReflectionstoGraphFunctions

5 UseVerticalStretchingandShrinkingtoGraphFunctions

6 UseHorizontalStretchingandShrinkingtoGraphFunctions

7 GraphFunctionsInvolvingaSequenceofTransformations

2.6 CombinationsofFunctions;CompositeFunctions

1 FindtheDomainofaFunction

2 CombineFunctionsUsingtheAlgebraofFunctions,SpecifyingDomains

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3 FormCompositeFunctions

4 DetermineDomainsforCompositeFunctions

5 WriteFunctionsasCompositions

2.7 InverseFunctions

1 VerifyInverseFunctions

2 FindtheInverseofaFunction

3 UsetheHorizontalLineTesttoDetermineifaFunctionhasanInverseFunction

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4 UsetheGraphofaOne–to–OneFunctiontoGraphItsInverseFunction

5 FindtheInverseofaFunctionandGraphBothFunctionsontheSameAxes

2.8 DistanceandMidpointFormulas;Circles

1 FindtheDistanceBetweenTwoPoints

2 FindtheMidpointofaLineSegment

3 WritetheStandardFormofaCircleʹsEquation

4 GivetheCenterandRadiusofaCircleWhoseEquationisinStandardForm

5 ConverttheGeneralFormofaCircleʹsEquationtoStandardForm

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