Elementary Education Chapter 3 If it is a function, state the domain and range.

Ch.3 FunctionsandTheirGraphs

3.1 Functions

1 DetermineWhetheraRelationRepresentsaFunction

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

Determinewhethertherelationrepresentsafunction.Ifitisafunction,statethedomainandrange.

1)



5→15

9→27

13 →39

17 →51

A) function

domain:{5,9,13,17}

range:{15,27,39,51}

B) function

domain:{15,27,39,51}

range:{5,9,13,17}

C) notafunction

2)



Alice

Brad

Carl



snake

cat

dog

A) function

domain:{Alice,Brad,Carl}

range:{snake,cat,dog}

B) function

domain:{snake,cat,dog}

range:{Alice,Brad,Carl}

C) notafunction

3)



Alice

Brad

Carl



cat

dog

A) function

domain:{Alice,Brad,Carl}

range:{cat,dog}

B) function

domain:{cat,dog}

range:{Alice,Brad,Carl}

C) notafunction

4) {(–3

,

–8),(0

,

5),(5

,

–3),(7

,

–1)}

A) function

domain:{–3,0,5,7}

range:{–8,5,–3,–1}

B) function

domain:{–8,5,–3,–1}

range:{–3,0,5,7}

C) notafunction

5) {(1

,

–4),(–3

,

–3),(–3

,

0),(6

,

3),(22

,

5)}

A) function

domain:{1,6,–3,22}

range:{–4,–3,0,3,5}

B) function

domain:{–4,–3,0,3,5}

range:{1,6,–3,22}

C) notafunction

6) {(–3

,

4),(–2

,

–1),(0,–5),(2

,

–1),(4

,

11)}

A) function

domain:{–3,–2,0,2,4}

range:{4,–1,–5,11}

B) function

domain:{4,–1,–5,11}

range:{–3,–2,0,2,4}

C) notafunction

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7) {(8.55,17.85),(8.555,–17.8),(7

3,0),(2.33,–8)}

A) function

domain:{8.55,8.555,7

3,2.33}

range:{17.85,–17.8,0,–8}

B) function

domain:{17.85,–17.8,0,–8}

range:{8.55,8.555,7

3,2.33}

C) notafunction

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

8) y=x4

A) function B) notafunction

9) y=1

x

A) function B) notafunction

10) y=|x|

A) function B) notafunction

11) y2=4–x2

A) function B) notafunction

12) y=±1–5x

A) function B) notafunction

13) x=y2

A) function B) notafunction

14) y2+x=2

A) function B) notafunction

15) y=4x2–3x+7

A) function B) notafunction

16) y=3x+2

x–1

A) function B) notafunction

17) x2+4y2=1

A) function B) notafunction

18) x–5y=2

A) function B) notafunction

19) 9x+x2+39=y

A) function B) notafunction

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2 FindtheValueofaFunction

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

Findthevalueforthefunction.

1) Findf(–2)whenf(x)=x2–3x–2.

A) 8 B) 12 C) 0 D) –4

2) Findf(–1)whenf(x)=x2–8

x–3

.

A) 7

4B) –9

4C) –1

4D) –9

2

3) Findf(–9)whenf(x)=|x|–6.

A) 3 B) –15 C) 15 D) –3

4) Findf(4)whenf(x)=x2+7x.

A) 2 11 B) 65 C) 2 14 D) 23

5) Findf(–x)whenf(x)=2x2+3x–2.

A) 2x2–3x–2B)

–2x2–3x+2C)2x

2–3x+2D)

–2x2–3x–2

6) Findf(–x)whenf(x)=x

x2+9

.

A) –x

x2+9

B) –x

x2–9

C) x

–x2+9

D) –x

–x2+9

7) Find–f(x)whenf(x)=2x2–5x–1.

A) –2x2+5x+1B)2x

2+5x–1C)2x

2+5x+1D)

–2x2+5x–1

8) Find–f(x)whenf(x)=|x|–8.

A) –|x|+8B)|

–x|–8C)

–|x|–8D)|

–x|+8

9) Findf(x–1)whenf(x)=3x2–4x+3.

A) 3x2–10x+10 B) –10x2+3x+10 C) 3x2–10x+2D)3x

2+5x+2

10) Findf(x+1)whenf(x)=x2–6

x+3.

A) x2+2x–5

x+4B) x2+2x+7

x+4C) x2+2x–5

x–2D) x2–5

x+4

11) Findf(–x)whenf(x)=3x2+2x+3.

A) 3x2–2x+3B)

–3x2–2x+3C)

–3x2–2x–3D)3x

2–2x–3

12) Findf(2x)whenf(x)=6x2–5x.

A) 24x2–10x B) 2 6x2–5x C) 12x2–10x D) 12x2–20x

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13) Findf(x+h)whenf(x)=–2x2–3x+3.

A) –2x2–4xh–2h2–3x–3h+3B)

–2x2–2h2–3x–3h+3

C) –2x2–2h2–7x–7h+3D)

–2x2–2xh–2h2–3x–3h+3

14) Findf(x+h)whenf(x)=7x+5

4x–9.

A) 7x+7h+5

4x+4h–9B) 7x+7h+5

4x–9C) 7x+12h

4x–5h D) 7x+5h

4x–9h

Solvetheproblem.

15) Iff(x)=8x3+5x2–x+Candf(2)=1,whatisthevalueofC?

A) C=–81 B) C=–13 C) C=47 D) C=87

16) Iff(x)=x–B

x–A,f(8)=0,andf(–6)isundefined,whatarethevaluesofAandB?

A) A=–6

,

B=8B)A=8

,

B= –6C)A=6

,

B= –8D)A= –8

,

B=6

17) Iff(x)=x–2A

6x+1

andf(6)=–6,whatisthevalueofA?

A) A=114 B) A=–114 C) A= –34 D) A=34

18) Ifarockfallsfromaheightof80metersonEarth,theheightH(inmeters)afterxsecondsis

approximately

H(x)=80–4.9x2.

Whatistheheightoftherockwhenx=1.4seconds?Roundtothenearesthundredth,ifnecessary.

A) 70.4m B) 89.6 m C) 73.14 m D) 70.59 m

19) Ifarockfallsfromaheightof40metersonEarth,theheightH(inmeters)afterxsecondsis

approximately

H(x)=40–4.9x2.

Whendoestherockstriketheground?Roundtothenearesthundredth,ifnecessary.

A) 2.86sec B) 8.16 sec C) 1.29 sec D) 1.67 sec

20) Ithasbeendeterminedthatthenumberoffishf(t)thatcanbecaughtintminutesinacertainpondusinga

certainbaitisf(t)=0.29t+1,fort>10.Findtheapproximatenumberoffishthatcanbecaughtifyoufish

for27minutes.

A) About8fish B) About19 fish C) About29 fish D) About31 fish

21) ThefunctionP(d)=1+d

33

givesthepressure,inatmospheres(atm),atadepthdfeetinthesea.Findthe

pressureat51feet.

A) 28

11

atm B) 17

11

atm C) 6

11

atm D) 52

33

atm

22) ThefunctionFdescribedbyF(C)=9

5C+32givestheFahrenheittemperaturecorrespondingtotheCelsius

temperatureC.FindtheFahrenheittemperatureequivalentto25°C.

A) 77°F B) 122°F C) 167°F D) 212°F

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3 FindtheDomainofaFunctionDefinedbyanEquation

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

Findthedomainofthefunction.

1) f(x)=3x–7

A) allrealnumbers B) {x|x≥7} C) {x|x≠0} D) {x|x>0}

2) f(x)=x2+4

A) allrealnumbers B) {x|x≥–4} C) {x|x> –4} D) {x|x≠–4}

3) f(x)=x

x2+7

A) allrealnumbers B) {x|x≠–7} C) {x|x> –7} D) {x|x≠0}

4) g(x)=2x

x2–36

A) {x|x≠–6

,

6} B) {x|x≠0} C) {x|x>36} D) allrealnumbers

5) h(x)=x–2

x3–36x

A) {x|x≠–6

,

0,6} B) {x|x≠0} C) {x|x≠2} D) allrealnumbers

6) f(x)=18–x

A) {x|x≤18} B) {x|x≠18} C) {x|x≤32} D) {x|x≠32}

7) x

x–1

A) {x|x>1} B) {x|x≥1} C) {x|x≠1} D) allrealnumbers

4 FormtheSum,Difference,Product,andQuotientofTwo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requestedfunctionandstateitsdomain.

1) f(x)=4–4x;g(x)=–9x+4

Findf+g.

A) (f+g)(x)=–13x+8;allrealnumbers B) (f+g)(x)=–9x+4;{x|x≠4

9}

C) (f+g)(x)=–5x;allrealnumbers D) (f+g)(x)=5x+8;{x|x≠8

5}

2) f(x)=8x–2;g(x)=2x–9

Findf–g.

A) (f–g)(x)=6x+7;allrealnumbers B) (f–g)(x)=6x–11;{x|x≠11

6}

C) (f–g)(x)=10x–11;{x|x≠1} D) (f–g)(x)= –6x–7;allrealnumbers

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3) f(x)=9x+8;g(x)=6x+7

Findf·g.

A) (f·g)(x)=54x2+111x+56;allrealnumbers B) (f·g)(x)=54x2+55x+56;{x|x≠56}

C) (f·g)(x)=15x2+111x+15;allrealnumbers D) (f·g)(x)=54x2+56;{x|x≠56}

4) f(x)=5x+3;g(x)=4x–5

Findf

g.

A) f

g(x)=5x+3

4x–5; x|x≠5

4B) f

g(x)=5x+3

4x–5; x|x≠–3

5

C) f

g(x)=4x–5

5x+3; x|x≠5

4D) f

g(x)=4x–5

5x+3; x|x≠–3

5

5) f(x)=16–x2;g(x)=4–x

Findf+g.

A) (f+g)(x)=–x2–x+20;allrealnumbers

B) (f+g)(x)=4+x;{x|x≠–4}

C) (f+g)(x)=–x2+x+12;allrealnumbers

D) (f+g)(x)=x3–4x2–16x+64;allrealnumbers

6) f(x)=x–3;g(x)=7x2

Findf–g.

A) (f–g)(x)=–7x2+x–3;allrealnumbers B) (f–g)(x)=7x2–x+3;allrealnumbers

C) (f–g)(x)=–7x2+x–3;{x|x≠3} D) (f–g)(x)=7x2+x–3;allrealnumbers

7) f(x)=5x3+3;g(x)=2x2+3

Findf·g.

A) (f·g)(x)=10x5+15x3+6x2+9;allrealnumbers

B) (f·g)(x)=10x6+15x3+6x2+9;allrealnumbers

C) (f·g)(x)=10x5+15x3+6x2+9;{x|x≠0}

D) (f·g)(x)=5x3+2x2+9;allrealnumbers

8) f(x)=x;g(x)=5x–8

Findf

g.

A) f

g(x)=x

5x–8; x|x≥0,x≠8

5B) f

g(x)=x

5x–8; x|x≠8

5

C) f

g(x)=x

5x–8;{x|x≠0} D) f

g(x)=5x–8

x;{x|x≥0}

9) f(x)=8–x;g(x)=x–1

Findf·g.

A) (f·g)(x)=(8–x)(x–1);{x|1≤x≤8} B) (f·g)(x)=(8–x)(x–1);{x|x≥0}

C) (f·g)(x)=(8–x)(x–1);{x|x≠1,x≠8} D) (f·g)(x)=–x2–8;{x|x≠8}

Page6

10) f(x)=8x–1

5x–9;g(x)=6x

5x–9

Findf+g.

A) (f+g)(x)=14x–1

5x–9; x|x≠9

5B) (f+g)(x)=2x+1

5x–9; x|x≠9

5

C) (f+g)(x)=14x–1

5x–9; x|x≠9

5,x≠1

14 D) (f+g)(x)=14x–1

5x–9;{x|x≠0}

11) f(x)=x+13;g(x)=3

x

Findf·g.

A) (f·g)(x)=3x+13

x;{x|x≥–13,x≠0} B) (f·g)(x)=3x+39

x;{x|x≥–13,x≠0}

C) (f·g)(x)=3x+39

x;{x|x≥–13,x≠0} D) (f·g)(x)=16

x;{x|x≠0}

Solvetheproblem.

12) Givenf(x)=1

x

and(f

g)(x)=x+4

x2+2x

,findthefunctiong.

A) g(x)=x+2

x+4B) g(x)=x+4

x+2C) g(x)=x–2

x–4D) g(x)=x–4

x–2

13) Find(f+g)(–5)whenf(x)=x–1andg(x)=x+6.

A) –5B)

–3C)

–17 D) –15

14) Find(f–g)(–5)whenf(x)=4x2–2andg(x)=x+7.

A) 96 B) –93 C) 110 D) 86

15) Find(fg)(3)whenf(x)=x–2andg(x)=–5x2+16x–6.

A) –3B)

–255 C) –15 D) 51

16) Findf

g(–2)whenf(x)=3x–3andg(x)=2x2+14x+2.

A) 1

2B) –1

9C) 2

3D) 0

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

h,h≠0,forthefunction.

17) f(x)=2x–3

A) 2 B) 2+–6

hC) 2+4(x–3)

hD) 0

18) f(x)=6x2

A) 6(2x+h) B) 12

h

+x+6h C) 6(2x2+2xh+h2)

hD) 6

19) f(x)=3

A) 0 B) 1 C) 1+6

hD) 3

Page7

20) f(x)=1

3x

A) –1

3x(x+h) B) –1

x(x+h) C) 1

3x D) 0

21) f(x)=x2+6x+8

A) 2x+h+6B)

2x2+2x+2xh+h2+h+16

h

C) 2x+h+8D)1

Solvetheproblem.

22) ExpressthegrosssalaryGofapersonwhoearns$12 perhourasafunctionofthenumberxofhours

worked.

A) G(x)=12x B) G(x)=12 +x C) G(x)=12

xD) G(x)=12x2

23)

J

acey,acommissionedsalesperson,earns$130 basepayplus$31 peritemsold.ExpressJaceyʹsgross

salaryGasafunctionofthenumberxofitemssold.

A) G(x)=31x+130 B) G(x)=130x+31 C) G(x)=31(x+130) D) G(x)=130(x+31)

24) SupposethatP(x)representsthepercentageofincomespentonfood inyearxandI(x)representsincome

inyearx.DetermineafunctionFthatrepresentstotalfoodexpendituresinyearx.

A) F(x)=(P·I)(x) B) F(x)=(P+I)(x) C) F(x)=(I–P)(x) D) F(x)=I

P(x)

25) Aretailstorebuys110VCRsfromadistributoratacostof$180 eachplusanoverheadchargeof$40 per

order.Theretailmarkupis45%onthetotalpricepaid.FindtheprofitonthesaleofoneVCR.

A) $81.16 B) $8116.00 C) $81.00 D) $80.84

Page8

26) Thefollowinggraphshowstheprivate,publicandtotalnationalschoolenrollmentforstudentsforselec

t

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

27) 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)=50x+3230.

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

R(x)=60x,

butthatnomorethan421unitscanbesoldatthatprice.Findandinterpret(R–C)(421).

A) $980profit,incomeexceedscos

t

Itisworthittodevelopproduct.

B) –$980 loss,costexceedsincome

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

C) $49,540profit,incomeexceedscos

t

Itisworthittodevelopproduct.

D) $744 profit,incomeexceedscos

t

Itisworthittodevelopproduct.

28) Thefunctionf(t)=–0.14t2+0.49t+31.8modelstheU.S.populationinmillions,ages65andolder,wheret

representsyearsafter1990.Thefunctiong(t)=0.55t2+11.24t+106.4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(5).

A) Costperpersoninthousandsofdollars.$5.73 thousand

B) Costperpersoninthousandsofdollars.$0.21 thousand

C) Costperpersoninthousandsofdollars.$0.17 thousand

D) Costperpersoninthousandsofdollars.$11.76 thousand

Page9

3.2 TheGraphofaFunction

1 IdentifytheGraphofaFunction

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

Determinewhetherthegraphisthatofafunction.Ifitis,usethegraphtofinditsdomainandrange,theintercepts,

ifany,andanysymmetrywithrespecttothex–axis,they–axis,ortheorigin.

1)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) function

domain:{x|x≤–3orx≥3}

range:allrealnumbers

intercepts:(–3,0),(3,0)

symmetry:x–axis,y–axis,origin

B) function

domain:allrealnumbers

range:{y|y≤–3ory≥3}

intercepts:(–3,0),(3,0)

symmetry:y–axis

C) function

domain:{x|–3≤x≤3}

range:allrealnumbers

intercepts:(–3,0),(3,0)

symmetry:x–axis,y–axis

D) notafunction

Page10

2)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

A) function

domain:{x|x>0}

range:allrealnumbers

intercept:(1,0)

symmetry:none

B) function

domain:{x|x>0}

range:allrealnumbers

intercept:(0,1)

symmetry:origin

C) function

domain:allrealnumbers

range:{y|y>0}

intercept:(1,0)

symmetry:none

D) notafunction

3)

x

–-3

4–

2–

4



4



23

4

y

1

-1

x

–-3

4–

2–

4



4



23

4

y

1

-1

A) function

domain:{x|–π≤x≤π}

range:{y|–1≤y≤1}

intercepts:(–π,0),(0,0),(π,0)

symmetry:origin

B) function

domain:{x|–1≤x≤1}

range:{y|–π≤y≤π}

intercepts:(–π,0),(0,0),(π,0)

symmetry:none

C) function

domain:allrealnumbers

range:{y|–1≤y≤1}

intercepts:(–π,0),(0,0),(π,0)

symmetry:origin

D) notafunction

Page11

4)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) function

domain:allrealnumbers

range:{y|y≤4}

intercepts:(–1,0),(0,3),(3,0)

symmetry:none

B) function

domain:{x|x≤4}

range:allrealnumbers

intercepts:(–1,0),(0,3),(3,0)

symmetry:y–axis

C) function

domain:allrealnumbers

range:{y|y≤4}

intercepts:(0,–1),(3,0),(0,3)

symmetry:none

D) notafunction

5)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) function

domain:{x|–3≤x≤3}

range:{y|–3≤y≤3}

intercepts:(–3,0),(0,–3),(0,3),(3,0)

symmetry:x–axis,y–axis,origin

B) function

domain:{x|–3≤x≤3}

range:{y|–3≤y≤3}

intercepts:(–3,0),(0,–3),(0,3),(3,0)

symmetry:x–axis,y–axis

C) function

domain:{x|–3≤x≤3}

range:{y|–3≤y≤3}

intercepts:(–3,0),(0,–3),(0,0),(0,3),(3,0)

symmetry:origin

D) notafunction

Page12

6)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

A) function

domain:{x|x≥–2}

range:{y|y≥0}

intercepts:(–2,0),(0,2),(2,0)

symmetry:none

B) function

domain:{x|x≥0}

range:{y|y≥–2}

intercepts:(–2,0),(0,2),(2,0)

symmetry:y–axis

C) function

domain:allrealnumbers

range:allrealnumbers

intercepts:(–2,0),(0,2),(2,0)

symmetry:none

D) notafunction

7)

x

-10 -5 5

y

10

5

-5

-10

x

-10 -5 5

y

10

5

-5

-10

A) function

domain:allrealnumbers

range:{y|y=8ory=5}

intercept:(0,5)

symmetry:none

B) function

domain:{x|x=8orx=5}

range:allrealnumbers

intercept:(5,0)

symmetry:x–axis

C) function

domain:allrealnumbers

range:allrealnumbers

intercept:(0,5)

symmetry:none

D) notafunction

Page13

2 ObtainInformationfromorabouttheGraphofaFunction

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) Usethegraphoffgivenbelowtofindf(–6).

10

–10 10

–10

A) 0 B) –6C)10D)

–4

2) Isf(–5)positiveornegative?

5

–55

–5

A) positive B) negative

Page14

3) Isf(3)positiveornegative?

5

–55

–5

A) positive B) negative

4) Forwhatnumbersxisf(x)=0?

10

–10 10

–10

A) –6

,

7

,

10 B) (–10

,

–6),(7

,

10) C) (–6

,

7) D) –6

Page15

5) Forwhatnumbersxisf(x)>0?

5

–55

–5

A) [–5

,

–3),(3.5

,

5) B) (–3

,

3.5) C) (–3

,

∞)D)(

–∞–3)

6) Forwhatnumbersxisf(x)

<

0?

50

–50 50

–50

A) (–30

,

35) B) [–50

,

–30),(35

,

50) C) (–30

,

∞)D)(

–∞

,

–30)

Page16

7) Whatisthedomainoff?

20

–20 20

–20

A) {x|–20≤x≤20} B) {x|–16 ≤x≤22} C) allrealnumbers D) {x|x≥0}

8) Whatarethex–intercepts?

50

–50 50

–50

A) –30

,

35

,

50 B) –50

,

–30

,

35

,

50 C) –30

,

35 D) –30

Page17

9) Whatisthey–intercept?

50

–50 50

–50

A) –30 B) 35 C) 50 D) –40

10) Howoftendoestheliney=–100intersectthegraph?

100

–100 100

–100

A) once B) twice C) threetimes D) doesnotintersec

t

Page18

11) Howoftendoestheliney=5intersectthegraph?

25

–25 25

–25

A) once B) twice C) threetimes D) doesnotintersec

t

12) Forwhichofthefollowingvaluesofxdoesf(x)=60?

100

–100 100

–100

A) –100 B) 160 C) 0 D) 60

Answerthequestionaboutthegivenfunction.

13) Giventhefunctionf(x)=7x2+14x–6,isthepoint(–1,–13)onthegraphoff?

A) Yes B) No

14) Giventhefunctionf(x)=–6x2–12x–6,isthepoint(–2,–18)onthegraphoff?

A) Yes B) No

15) Giventhefunctionf(x)=–3x2+6x–7,ifx=1,whatisf(x)?Whatpointisonthegraphoff?

A) –4;(1

,

–4) B) –4;(–4

,

1) C) –16;(1

,

–16) D) –16;(–16

,

1)

16) Giventhefunctionf(x)=2x2–4x–4,whatisthedomainoff?

A) allrealnumbers B) {x|x≥1} C) {x|x≤1} D) {x|x≥–1}

17) Giventhefunctionf(x)=x2+2x–8,listthex–intercepts,ifany,ofthegraphoff.

A) (–4

,

0),(2

,

0) B) (4

,

0),(2

,

0) C) (–4

,

0),(1,0) D) (4

,

0),(–2

,

0)

Page19

18) Giventhefunctionf(x)=–3x2+6x+3,listthey–intercept,ifthereisone,ofthegraphoff.

A) 3 B) –3C)6 D)

–6

19) Giventhefunctionf(x)=x2–6

x+2,isthepoint(–1,–5)onthegraphoff?

A) Yes B) No

20) Giventhefunctionf(x)=x2–2

x+3,isthepoint(2,6

5)onthegraphoff?

A) Yes B) No

21) Giventhefunctionf(x)=x2–8

x–3,ifx=1,whatisf(x)?Whatpointisonthegraphoff?

A) 7

2;(1,7

2)B)

7

2;(7

2,1) C) –9

2;(1,–9

2)D)

–9

2;(–9

2,1)

22) Giventhefunctionf(x)=x2+6

x+4,whatisthedomainoff?

A) {x|x≠–4} B) {x|x≠4} C) {x|x≠6} D) {x|x≠–3

2}

23) Giventhefunctionf(x)=x2+2

x+7,listthex–intercepts,ifany,ofthegraphoff.

A) (2

,

0),(–2

,

0) B) (–7

,

0) C) (–2,0) D) none

24) Giventhefunctionf(x)=x2+3

x+2,listthey–intercept,ifthereisone,ofthegraphoff.

A) (0,3

2)B)(

3

2,0) C) (0,–2) D) (0,–3)

Solvetheproblem.

25) Ifanobjectweighsmpoundsatsealevel,thenitsweightW(inpounds)ataheightofhmilesabovesea

levelisgivenapproximatelybyW(h)=m4000

4000+h

2.Howmuchwillamanwhoweighs165poundsat

sealevelweighonthetopofamountainwhichis14,494feetabovesealevel?Roundtothenearest

hundredthofapound,ifnecessary.

A) 164.77pounds B) 7.72pounds C) 165.23pounds D) 165pounds

Page20

Matchthefunctionwiththegraphthatbestdescribesthesituation.

26) Theamountofrainfallasafunctionoftime,iftherainfellmoreandmoresoftly.

A)

x

y

x

y

B)

x

y

x

y

C)

x

y

x

y

D)

x

y

x

y

Page21

27) Theheightofananimalasafunctionoftime.

A)

x

y

x

y

B)

x

y

x

y

C)

x

y

x

y

D)

x

y

x

y

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

Solvetheproblem.

28) Michaeldecidestowalktothemalltodosomeerrands.Heleaveshome,walks5blocksin16 minutesata

constantspeed,andrealizesthatheforgothiswalletathome.SoMichaelrunsbackin11minutes.At

home,ittakeshim3minutestofindhiswalletandclosethedoor.Michaelwalks3blocksin12minutes

andthendecidestojogtothemall.Ittakeshim9minutestogettothemallwhichis4blocksaway.Draw

agraphofMichaelʹsdistancefromhome(inblocks)asafunctionoftime.

x

y

x

y

Page22

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

29) Asteelcanintheshapeofarightcircularcylindermustbedesignedtohold350cubiccentimetersofjuice

(seefigure).Itcanbeshownthatthetotalsurfaceareaofthecan(includingtheends)isgivenbyS(r)=2π

r2+700

r,whereristheradiusofthecanincentimeters.UsingtheTABLEfeatureofagraphingutility,

findtheradiusthatminimizesthesurfacearea(andthusthecost)ofthecan.Roundtothenearesttenthof

acentimeter.

A) 3.8cm B) 5cm C) 3 cm D) 0cm

30) TheconcentrationC(arbitraryunits)ofacertaindruginapatientʹsbloodstreamcanbemodeledusing

C(t)=t

0.535t+1.871 2,wheretisthenumberofhourssincea500milligramoraldosewasadministered.

UsingtheTABLEfeatureofagraphingutility,findthetimeatwhichtheconcentrationofthedrugis

greatest.Roundtothenearesttenthofanhour.

A) 3.5hours B) 5hours C) 4.3 hours D) 5.8hours

3.3 PropertiesofFunctions

1 DetermineEvenandOddFunctionsfromaGraph

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

Thegraphofafunctionisgiven.Decidewhetheritiseven,odd,orneither.

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) even B) odd C) neither

Page23

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) even B) odd C) neither

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) even B) odd C) neither

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) even B) odd C) neither

Page24

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) even B) odd C) neither

6)

x

–10–8–6–4–2 246810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8–6–4–2 246810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A) even B) odd C) neither

7)

x

––

2



2

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

––

2



2

y

5

4

3

2

1

-1

-2

-3

-4

-5

A) even B) odd C) neither

Page25

8)

x

––

2



2

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

––

2



2

y

5

4

3

2

1

-1

-2

-3

-4

-5

A) even B) odd C) neither

2 IdentifyEvenandOddFunctionsfromtheEquation

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

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

1) f(x)=3x3

A) even B) odd C) neither

2) f(x)=–5x4–x2

A) even B) odd C) neither

3) f(x)=–2x2–9

A) even B) odd C) neither

4) f(x)=4x3+6

A) even B) odd C) neither

5) f(x)=3x

A) even B) odd C) neither

6) f(x)=x

A) even B) odd C) neither

7) 35x2+9

A) even B) odd C) neither

8) f(x)=1

x2

A) even B) odd C) neither

9) f(x)=x

x2+4

A) even B) odd C) neither

Page26

10) f(x)=–x3

5x2–6

A) even B) odd C) neither

11) f(x)=3x

|x|

A) even B) odd C) neither

3 UseaGraphtoDetermineWhereaFunctionIsIncreasing,Decreasing,orConstant

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

Thegraphofafunctionisgiven.Determinewhetherthefunctionisincreasing,decreasing,orconstantonthegiven

interval.

1) (–3,–3

2)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

A) decreasing B) increasing C) constant

2) (–1

,

0)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

A) increasing B) decreasing C) constant

Page27

3) (0,1)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

A) decreasing B) increasing C) constant

4) (1,5)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

A) increasing B) decreasing C) constant

5) (0,1)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) constant B) increasing C) decreasing

Page28

6) (–2

,

0)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) increasing B) decreasing C) constant

7) (2

,

∞)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) decreasing B) increasing C) constant

8) (0

,

∞)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) increasing B) decreasing C) constant

Page29

9) (–1

,

1)

x

-2 -1 1 2

y

3

2

1

-1

-2

-3

x

-2 -1 1 2

y

3

2

1

-1

-2

-3

A) decreasing B) increasing C) constant

10) (–3

,

–4)

x

-5 5

y

5

-5

(-5, –2) (-4, –2)

(0.5, 1.5) (3.5, 1.5)

(6, -1.3)

x

-5 5

y

5

-5

(-5, –2) (-4, –2)

(0.5, 1.5) (3.5, 1.5)

(6, -1.3)

A) constant B) increasing C) decreasing

11) (2

,

5)

x

-5 5

y

5

-5

(-6, 2)

(-2.5, 0)

(-1, –2) (0, –2)

(2, 0)

(5, –4)

x

-5 5

y

5

-5

(-6, 2)

(-2.5, 0)

(-1, –2) (0, –2)

(2, 0)

(5, –4)

A) decreasing B) increasing C) constant

Page30

12) (5

,

∞)

x

-10 10

y

10

-10

(-8, 5)

(-5, 0)

(0, 0)

(4, 0)

(5, -2.5)

(-9.5, 0)

(-2.5, –3.3)

(2.2, 3.9)

x

-10 10

y

10

-10

(-8, 5)

(-5, 0)

(0, 0)

(4, 0)

(5, -2.5)

(-9.5, 0)

(-2.5, –3.3)

(2.2, 3.9)

A) increasing B) decreasing C) constant

Usethegraphtofindtheintervalsonwhichitisincreasing,decreasing,orconstant.

13)

A) Increasingon(–∞

,

0);decreasingon(0,∞) B) Decreasingon(–∞

,

0);increasingon(0,∞)

C) Decreasingon(–∞

,

∞) D) Increasingon(–∞

,

∞)

Page31

14)

A) Increasingon(–∞

,

∞) B) Decreasingon(–∞

,

0);increasingon(0,∞)

C) Decreasingon(–∞

,

∞) D) Increasingon(–∞

,

0);decreasingon(0,∞)

15)

A) Decreasingon–π,–π

2

andπ

2,π ;increasingon–π

2,π

2

B) Increasingon–π,–π

2

andπ

2,π ;decreasingon–π

2,π

2

C) Decreasingon–π

,

0 ;increasingon0,π

D) Increasingon(–∞

,

∞)

Page32

16)

A) Decreasingon(–3,–2)and(2,4);increasingon(–1,1);constanton(–2,–1)and(1,2)

B) Decreasingon(–3,–2)and(2,4);increasingon(–1,1)

C) Decreasingon(–3,–1)and(1,4);increasingon(–2,1)

D) Increasingon(–3,–2)and(2,4);decreasingon(–1,1);constanton(–2,–1)and(1,2)

4 UseaGraphtoLocateLocalMaximaandLocal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localmaximum.Whatarethelocal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localmaximumatx=0;thelocalmaximumis1

B) fhasalocalmaximumatx=–2 and2;thelocalmaximumis0

C) fhasalocalmaximumatx=2;thelocalmaximumis1

D) fhasnolocalmaximum

Page33

2) Findthenumbers,ifany,atwhichfhasalocalminimum.Whatarethelocal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localminimumatx=–2and2;thelocalminimumis0

B) fhasalocalminimumatx=0;thelocalminimumis1

C) fhasalocalminimumatx=–2;thelocalminimumis0

D) fhasnolocalminimum

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

x

–



–



2



2



y

2

1

-1

-2

x

–



–



2



2



y

2

1

-1

-2

A) fhasalocalmaximumatx=0;thelocalmaximumis1

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

C) fhasalocalmaximumat–π;thelocalmaximumis1

D) fhasnolocalmaximum

Page34

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

x

–



–



2



2



y

2

1

-1

-2

x

–



–



2



2



y

2

1

-1

-2

A) fhasalocalminimumatx=0;thelocalminimumis–2

B) fhasalocalminimumatx=–πandπ;thelocalminimumis2

C) fhasalocalminimumatx=–π;thelocalminimumis–2

D) fhasnolocalminimum

5)

x

-10 10

y

10

-10

(-8, 5)

(-5, 0)

(0, 0)

(4, 0)

(5, -2.5)

(-9.5, 0)

(-2.5, –3.3)

(2.2, 3.9)

x

-10 10

y

10

-10

(-8, 5)

(-5, 0)

(0, 0)

(4, 0)

(5, -2.5)

(-9.5, 0)

(-2.5, –3.3)

(2.2, 3.9)

Findthenumbers,ifany,atwhichfhasalocalminimum.Whatarethelocalmaxima?

A) fhasalocalminimumatx=–2.5 and5;thelocalminimum at–2.5 is–3.3;thelocalminimum at5 is

–2.5

B) fhasalocalminimumatx=–3.3 and–2.5;thelocalminimum at–3.3 is–2.5;thelocalminimum at

–2.5is5

C) fhasalocalmaximumatx=–2.5 and5;thelocalmaximum at–2.5 is–3.3;thelocalmaximum at5 is

–2.5

D) fhasalocalmaximumatx=–3.3 and–2.5;thelocalmaximum at–3.3 is–2.5;thelocalmaximum at

–2.5is5

Page35

Solvetheproblem.

6) Theheightsofaball(infeet)thrownwithaninitialvelocityof70 feetpersecondfromaninitialheighto

f

5feetisgivenasafunctionoftimet(inseconds)bys(t)=–16t2+70t+5.Whatisthemaximumheight?

Roundtothenearesthundredth,ifnecessary.

x

y

x

y

A) 81.56ft B) 92.5 ft C) 76.88 ft D) –54.37 ft

5 UseaGraphtoLocatetheAbsoluteMaximumandtheAbsoluteMinimum

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

Forthegraphofthefunctiony=f(x),findtheabsolutemaximumandtheabsoluteminimum,ifitexists.

1)

A) Absolutemaximum:f(5)=6;Absoluteminimum:f(2)=1

B) Absolutemaximum:f(7)=2;Absoluteminimum:f(0)=3

C) Absolutemaximum:f(6)=5;Absoluteminimum:f(1)=2

D) Absolutemaximum:f(2)=7;Absoluteminimum:f(3)=0

Page36

2)

A) Absolutemaximum:f(3)=6;Absoluteminimum:none

B) Absolutemaximum:f(3)=6;Absoluteminimum:f(5)=1

C) Absolutemaximum:f(7)=4;Absoluteminimum:f(0)=2

D) Absolutemaximum:f(3)=6;Absoluteminimum:f(0)=2

3)

A) Absolutemaximum:none;Absoluteminimum:f(1)=2

B) Absolutemaximum:f(–1)=6;Absoluteminimum:f(1)=2

C) Absolutemaximum:f(3)=5;Absoluteminimum:f(1)=2

D) Absolutemaximum:none;Absoluteminimum:none

Page37

4)

A) Absolutemaximum:none;Absoluteminimum:none

B) Absolutemaximum:f(4)=7;Absoluteminimum:f(1)=2

C) Absolutemaximum:none;Absoluteminimum:f(1)=2

D) Absolutemaximum:f(4)=7;Absoluteminimum:none

6 UseGraphingUtilitytoApproximateLocalMaxima/MinimaandtoDetermineWhereFunctionIsIncrs/Decrs

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

Useagraphingutilitytographthefunctionovertheindicatedintervalandapproximateanylocalmaximaandlocal

minima.Determinewherethefunctionisincreasingandwhereitisdecreasing.Ifnecessary,roundanswerstotwo

decimalplaces.

1) f(x)=x3–3x2+1,(–1,3)

A) localmaximumat(0

,

1)

localminimumat(2,–3)

increasingon(–1,0)and(2,3)

decreasingon(0,2)

B) localmaximumat(2

,

–3)

localminimumat(0,1)

increasingon(–1,0)and(2,3)

decreasingon(0,2)

C) localmaximumat(0

,

1)

localminimumat(2,–3)

increasingon(0,2)

decreasingon(–1,0)and(2,3)

D) localmaximumat(2

,

–3)

localminimumat(0,1)

increasingon(–1,0)

decreasingon(0,2)

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

2) f(x)=x3–4x2+6;(–1,4)

3) f(x)=x5–x2;(–2,2)

4) f(x)=–0.3x3+0.2x2+4x–5;(–4,5)

5) f(x)=0.15x4+0.3x3–0.8x2+5;(–4,2)

Page38

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

Useagraphingutilitytographthefunctionovertheindicatedintervalandapproximateanylocalmaximaandlocal

minima.Ifnecessary,roundanswerstotwodecimalplaces.

6) f(x)=x2+2x–3;(–5,5)

A) localminimumat(–1,–4) B) localmaximumat(–1,4)

C) localminimumat(1,4) D) localmaximumat(1,–4)

7) f(x)=2+8x–x2;(–5,5)

A) localmaximumat(4,18) B) localminimumat(4,50)

C) localminimumat(–4,18) D) localmaximumat(–4,50)

8) f(x)=x3–3x2+1;(–5,5)

A) localmaximumat(0,1)

localminimumat(2,–3)

B) localminimumat(0,1)

localmaximumat(2,–3)

C) localminimumat(2,–3) D) none

9) f(x)=x3–12x+2;(–5,5)

A) localmaximumat(–2,18)

localminimumat(2,–14)

B) localmaximumat(–2,18)

localminimumat(0,0)

localminimumat(2,–14)

C) localminimumat(0,0) D) none

10) f(x)=x4–5x3+3x2+9x–3;(–5,5)

A) localminimumat(–0.57,–6.12)

localmaximumat(1.32,5.64)

localminimumat(3,–3)

B) localminimumat(–1,–6)

localmaximumat(1,6)

localminimumat(3,–3)

C) localminimumat(–3,–3)

localmaximumat(–1.32,5.64)

localminimumat(0.57,–6.12)

D) localminimumat(–0.61,–5.64)

localmaximumat(1.41,6.12)

localminimumat(3,–3)

Solve.

11)

J

ohnownsahotdogstand.Hehasfoundthathisprofitisrepresentedbytheequation

P(x)=–x2+52x+70,withPbeingprofitsandxthenumberofhotdogssold.Howmanyhotdogsmusthe

selltoearnthemostprofit?

A) 26hotdogs B) 44hotdogs C) 27 hotdogs D) 22hotdogs

12) Bobownsawatchrepairshop.Hehasfoundthatthecostofoperatinghisshopisgivenby

c(x)=4x2–400x+65,whereciscostandxisthenumberofwatchesrepaired.Howmanywatchesmust

herepairtohavethelowestcost?

A) 50watches B) 40watches C) 65 watches D) 32watches

13) Johnownsahotdogstand.HisprofitisrepresentedbytheequationP(x)=–x2+10x+34,withPbeing

profitsandxthenumberofhotdogssold.Whatisthemosthecanearn?

A) $59 B) $39 C) $99 D) $25

Page39

14) Arockfallsfromatowerthatis142.1 mhigh.Asitisfalling,itsheightisgivenbytheformula

h(t)=142.1–4.9t2.Howmanysecondswillittakefortherocktohittheground(h=0)?Roundtothe

nearesttenth.

A) 5.4sec B) 11.9 sec C) 4100 sec D) 29.2 sec

15) Aprojectileisthrownupwardsothatitsdistanceabovethegroundaftertsecondsish(t)=–16t2+400t.

Afterhowmanysecondsdoesitreachitsmaximumheight?Roundtothenearestsecond.

A) 13sec B) 10sec C) 30 sec D) 40sec

16) Arockfallsfromatowerthatis224fthigh.Asitisfalling,itsheightisgivenbytheformula

h(t)=224–16t2.Howmanysecondswillittakefortherocktohittheground(h=0)?Roundtothenearest

tenth.

A) 3.7sec B) 15sec C) 3136 sec D) 13.7 sec

7 FindtheAverageRateofChangeofaFunction

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

Forthefunction,findtheaveragerateofchangeofffrom1tox:

f(x)–f(1)

x–1,x≠1

1) f(x)=–8x

A) –8B)

–9C)

–8

x–1D) 0

2) f(x)=x3+x

A) x2+x+2B)x

2+2C)1 D)

x3+x+2

x–1

3) f(x)=6

x+5

A) –1

x+5B) 1

x+5C) 6

(x–1)(x+5) D) 6

x(x+5)

4) f(x)=x+15

A) x+15–4

x–1B) x+15+4

x+1C) x+15–4

x+1D) x+15+4

x–1

Findtheaveragerateofchangeforthefunctionbetweenthegivenvalues.

5) f(x)=–3x+6;from1to2

A) –3B)

–6 C) 3 D) 6

6) f(x)=x2+6x;from5to8

A) 19 B) 112

3C) 57

8D) 14

7) f(x)=6x3+4x2–1;from–5to5

A) 150 B) 849

10 C) 300 D) 849

5

Page40

8) f(x)=2x;from2to8

A) 1

3B) 2 C) 7 D) –3

10

9) f(x)=3

x–2;from4to7

A) –3

10 B) 2 C) 7 D) 1

3

10) f(x)=4x2;from0to7

4

A) 7 B) 2 C) 1

3D) –3

10

11) f(x)=–3x2–x;from5to6

A) –34 B) –2C)

1

2D) –1

6

12) f(x)=x3+x2–8x–7;from0to2

A) –2B)

–28 C) 1

2D) –1

6

13) f(x)=2x–1;from1to5

A) 1

2B) –2C)

–28 D) –1

6

14) f(x)=3

x+2;from1to4

A) –1

6B) –2C)

–28 D) 1

2

Findanequationofthesecantlinecontaining(1,f(1))and(2,f(2)).

15) f(x)=x3+x

A) y=8x–6B)y=8x+6C)y= –8x–6D)y= –8x+6

16) f(x)=4

x+3

A) y=–1

5x+6

5B) y=1

5x+4

5C) y=4

5x+1

5D) y=1

5x+3

2

17) f(x)=x+35

A) y=(37–6)x–37+12 B) y=(–37+6)x+37–12

C) y=(37

–6)x+37–12 D) y=(–37–6)x–37+12

Page41

Solvetheproblem.

18) 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) 114

May 108

June 88

July 100

August 96

September 111

October 92

November 85

December 65

A) $7.67permonth B) –$7.67 permonth

C) $11.50permonth D) –$11.50 permonth

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

e

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

returnsfortheperiod1993to1998.Findtheaveragerateofchangebetween1995and1997.

Year CharitableContributions

1993 $1940

1994 $2420

1995 $2500

1996 $2780

1997 $3050

1998 $3160

A) $275peryear B) $550 peryear C) $330 peryear D) $315 peryear

20) Adeepseadivingbellisbeingloweredataconstantrate.After12 minutes,thebellisatadepthof400 ft.

After40minutesthebellisatadepthof1500ft.Whatistheaveragerateofloweringperminute?Round

tothenearesthundredthisneeded.

A) 39.3ftperminute B) 0.03 ftperminute C) 27.5 ftperminute D) 37.5 ftperminute

3.4 LibraryofFunctions;Piecewise–definedFunctions

1 GraphtheFunctionsListedintheLibraryofFunctions

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

Matchthegraphtothefunctionlistedwhosegraphmostresemblestheonegiven.

1)

A) squarefunction B) cubefunction

C) absolutevaluefunction D) reciprocalfunctio

n

Page42

2)

A) constantfunction B) linearfunction

C) absolutevaluefunction D) reciprocalfunctio

n

3)

A) squarerootfunction B) squarefunction

C) cuberootfunction D) cubefunction

4)

A) absolutevaluefunction B) squarefunction

C) linearfunction D) reciprocalfunctio

n

5)

A) linearfunction B) constantfunction

C) absolutevaluefunction D) reciprocalfunctio

n

6)

A) cubefunction B) cuberootfunction

C) squarefunction D) squarerootfunction

Page43

7)

A) reciprocalfunctio

n

B) squarerootfunction

C) absolutevaluefunction D) squarefunction

8)

A) cuberootfunction B) cubefunction

C) squarerootfunction D) squarefunction

Graphthefunction.

9) f(x)=x

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

Page44

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

10) f(x)=x2

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

Page45

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

11) f(x)=x3

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

Page46

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

12) f(x)=x



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

Page47

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

13) f(x)=1

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

Page48

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

14) f(x)=x



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

Page49

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

15) f(x)=3x



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

Page50

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

16) f(x)=–3

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51

2 GraphPiecewise–definedFunctions

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

Graphthefunction.

1)

f(x)=x–4ifx<1

5ifx≥1

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52

2)

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53

3)

f(x)=–x+2x<0

x+3x≥0

x

-5 5

y

x

-5 5

y

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54

4)

f(x)=

x+5if–8≤x<2

–6ifx=2

–x+4ifx>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

(-8, –3)

(2, 7)

(2, –6)

(2, 2)

x

-10 -5 5 10

y

10

5

-5

-10

(-8, –3)

(2, 7)

(2, –6)

(2, 2)

B)

x

-10 -5 5 10

y

10

5

-5

-10

(-8, –3)

(2, 7)

(2, –6)

(2, 2)

x

-10 -5 5 10

y

10

5

-5

-10

(-8, –3)

(2, 7)

(2, –6)

(2, 2)

C)

x

-10 -5 5 10

y

10

5

-5

-10

(-8, –2)

(2, 8)

(2, –6)

(2, 2)

x

-10 -5 5 10

y

10

5

-5

-10

(-8, –2)

(2, 8)

(2, –6)

(2, 2)

D)

x

-10 -5 5 10

y

10

5

-5

-10

(-8, –2)

(2, 8)

(2, –6)

(2, 2)

x

-10 -5 5 10

y

10

5

-5

-10

(-8, –2)

(2, 8)

(2, –6)

(2, 2)

5)

f(x)=

1if–1≤x<5

|x| if5≤x<9

xif9≤x≤14

Page55

x

-10 -5 5 10 15

y

10

5

-5

-10

x

-10 -5 5 10 15

y

10

5

-5

-10

A)

x

–10 -5 5 10 15

y

10

5

-5

-10

(-1, 1) (5, 1)

(5, 5)

(9, 9)

(9, 3) (14, 3.7)

x

–10 -5 5 10 15

y

10

5

-5

-10

(-1, 1) (5, 1)

(5, 5)

(9, 9)

(9, 3) (14, 3.7)

B)

x

-10 -5 5 10 15

y

10

5

-5

-10

(-1, 1) (5, 1)

(5, 5)

(9, 9)

(9, 3) (14, 3.7)

x

-10 -5 5 10 15

y

10

5

-5

-10

(-1, 1) (5, 1)

(5, 5)

(9, 9)

(9, 3) (14, 3.7)

C)

x

–10 -5 5 10 15

y

10

5

-5

-10

(-1, –1) (5, –1)

(5, 5)

(9, 9)

(9, 3) (14, 3.7)

x

–10 -5 5 10 15

y

10

5

-5

-10

(-1, –1) (5, –1)

(5, 5)

(9, 9)

(9, 3) (14, 3.7)

D)

x

-10 -5 5 10 15

y

10

5

-5

-10

(-1, –1) (5, –1)

(5, 5)

(9, 9)

(9, 3) (14, 3.7)

x

-10 -5 5 10 15

y

10

5

-5

-10

(-1, –1) (5, –1)

(5, 5)

(9, 9)

(9, 3) (14, 3.7)

Findthedomainofthefunction.

6)

f(x)=–3x ifx≠0

–5ifx=0

A) allrealnumbers B) {x|x≠0} C) {0} D) {x|x≤0}

7)

f(x)=

1if–8≤x<–2

|x| if–2≤x<8

xif8≤x≤28

A) {x|–8≤x≤28} B) {x|x≥–8}

C) {x|–8≤x

<

8or8

<

x≤28} D) {x|8 ≤x≤28}

Page56

Locateanyinterceptsofthefunction.

8)

f(x)=–3x+8ifx<1

8x–3ifx≥1

A) (0,8) B) (0,8),(8

3,0),(3

8,0)

C) (0,–3) D) (0,–3),(8

3,0),(3

8,0)

9)

f(x)=

1if–8≤x<–8

|x| if–8≤x<8

3xif8≤x≤17

A) (0,0) B) (0,0),(1,0) C) (0,0),(0,1) D) none

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

10)

f(x)=

1

2xifx≠0

4ifx=0

x

-10 -5 5

y

10

5

-5

-10

(0, 4)

x

-10 -5 5

y

10

5

-5

-10

(0, 4)

A) (–∞

,

0)or(0,∞)B)(

–∞

,

∞)

C) (–10,10) D) (–∞

,

0)or{0}or(0,∞)

Page57

11)

f(x)=

4if–6≤x<–3

|x| if–3≤x<6

xif6≤x≤14

x

–10 -5 5 10 15

y

10

5

-5

-10

(-6, 4) (–3, 4)

(-3, 3)

(6, 6)

(6, 2.4)

(14, 3.7)

x

–10 -5 5 10 15

y

10

5

-5

-10

(-6, 4) (–3, 4)

(-3, 3)

(6, 6)

(6, 2.4)

(14, 3.7)

A) [0,6) B) [0,∞) C) [0,14] D) [0,6]

Thegraphofapiecewise–definedfunctionisgiven.Writeadefinitionforthefunction.

12)

x

-5 5

y

5

-5

(-4, 2) (3, 3)

x

-5 5

y

5

-5

(-4, 2) (3, 3)

A)

f(x)=–1

2xif–4≤x≤0

xif0<x≤3

B)

f(x)=

1

2xif–4<x<0

xif0<x<3

C)

f(x)=–1

2xif–4<x<0

xif0<x<3

D)

f(x)=–2x if–4≤x≤0

xif0<x≤3

Page58

13)

x

-5 5

y

5

-5

(0, 1)

(3, 4)

(3, 2)

(5, 3)

x

-5 5

y

5

-5

(0, 1)

(3, 4)

(3, 2)

(5, 3)

A)

f(x)=

x+1if0≤x≤3

1

2x+1

2if3<x≤5

B)

f(x)=

x+1if0≤x≤3

1

2xif3<x≤5

C)

f(x)=

x+1if0≤x≤3

1

2x+2if3<x≤5

D)

f(x)=

x+1if0≤x≤3

1

2x–1

2if3<x≤5

14)

x

-5 5

y

5

-5

(-3, 0)

(0, 4)

(3, 2)

x

-5 5

y

5

-5

(-3, 0)

(0, 4)

(3, 2)

A)

f(x)=

4

3x+4if–3≤x≤0

2

3xif0<x≤3

B)

f(x)=

3

4x+4if–3≤x≤0

3

2xif0<x≤3

C)

f(x)=

4

3x–4if–3≤x≤0

2

3xif0≤x≤3

D)

f(x)=

4

3x+4if–3≤x≤0

2

3x+2if0<x≤3

Page59

15)

x

-5 5

y

5

-5

(-3, 0)

(0, 4)

(3, 2)

x

-5 5

y

5

-5

(-3, 0)

(0, 4)

(3, 2)

A)

f(x)=

4

3x+4if–3≤x≤0

2

3xifx>0

B)

f(x)=

3

4x+4if–3≤x≤0

3

2xifx>0

C)

f(x)=

3

4x+4if–3≤x≤0

3

2xifx≥0

D)

f(x)=

4

3x+4if–3≤x≤0

2

3xif0<x≤3

Solvetheproblem.

16) Iff(x)=int(3x),findf(1.8).

A) 5 B) 6 C) 2 D) 1

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

17) 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.

Page60

18) 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.

19) OneInternetserviceproviderhasthefollowingratescheduleforhig

h

–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?

20) 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.)

21) 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.

Page61

3.5 GraphingTechniques:Transformations

1 GraphFunctionsUsingVerticalandHorizontalShifts

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

Matchthecorrectfunctiontothegraph.

1)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

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

2)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

A) y=|2–x| B) y=|x+2| C) y=|1–x| D) y=x–2

Writetheequationofasinefunctionthathasthegivencharacteristics.

3) Thegraphofy=x2,shifted8unitsupward

A) y=x2+8B)y=x2–8C)y=x2

8D) y=8x2

4) Thegraphofy=x

,

shifted5unitstotheleft

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

5) Thegraphofy=x

,

shifted9unitsupward

A) y=x+9B)y=x–9 C) y=x+9 D) y=x–9

6) Thegraphofy=x,shifted2unitstotheright

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

7) Thegraphofy=x,shifted5unitstotheleft

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

Page62

8) Thegraphofy=x,shifted6unitsupward

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

9) Thegraphofy=x,shifted7unitsdownward

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

Supposethepoint(2,4)isonthegraphofy=f(x).Findapointonthegraphofthegivenfunction.

10) y=f(x+5)

A) (–3

,

4) B) (7

,

4) C) (2,–1) D) (2,9)

11) f(x)+2

A) (2,6) B) (2,–2) C) (4

,

4) D) (0

,

4)

Solvetheproblem.

12) Supposethatthex–interceptsofthegraphofy=f(x)are3 and5.Whatarethex–interceptso

f

y=f(x+6)?

A) –3and–1B)9and11 C) 18 and30 D) 3and11

13) Supposethatthex–interceptsofthegraphofy=f(x)are8 and9.Whatarethex–interceptso

f

y=f(x–7)?

A) 15and16 B) 1and2C)56and63 D) 8and2

14) Supposethatthefunctiony=f(x)isincreasingontheinterval(4

,

5).Overwhatintervalisthegraphof

y=f(x+8)increasing?

A) (–4

,

–3) B) (12

,

13) C) (32

,

40) D) (4

,

5)

15) Supposethatthefunctiony=f(x)isincreasingontheinterval(6

,

7).Overwhatintervalisthegraphof

y=f(x–3)increasing?

A) (9

,

10) B) (3

,

4) C) (18 ,21) D) (6

,

7)

Graphthefunctionbystartingwiththegraphofthebasicfunctionandthenusingthetechniquesofshifting,

compressing,stretching,and/orreflecting.

16) f(x)=x2+4

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page63

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64

17) f(x)=(x–1)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

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65

18) f(x)=(x+1)2–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

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66

19) f(x)=x3–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

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67

20) f(x)=(x–4)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

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68

21) f(x)=(x–4)3–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

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69

22) f(x)=x–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

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70

23) f(x)=x–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

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71

24) f(x)=x+4–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

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72

25) f(x)=x+1–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

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73

26) f(x)=|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

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74

27) f(x)=|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

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75

28) f(x)=|x+1|+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

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

29) f(x)=1

x

+5

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page76

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

30) f(x)=1

x+2

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page77

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78

31) f(x)=1

x+1

+6

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79

Usingtransformations,sketchthegraphoftherequestedfunction.

32) Thegraphofafunctionfisillustrated.Usethegraphoffasthefirststeptowardgraphingthefunction

F(x),whereF(x)=f(x+2)–1.

x

-5 5

y

5

-5

(-3, –2)

(-1, 1)

(3, –4)

x

-5 5

y

5

-5

(-3, –2)

(-1, 1)

(3, –4)

A)

x

-5 5

y

5

-5

(-5, –3)

(-3, 0)

(1, –5)

x

-5 5

y

5

-5

(-5, –3)

(-3, 0)

(1, –5)

B)

x

-5 5

y

5

-5

(-1, –3)

(1, 0)

(5, –5

)

x

-5 5

y

5

-5

(-1, –3)

(1, 0)

(5, –5

)

C)

x

-5 5

y

5

-5

(-5, –1)

(-3, 2)

(1, –3)

x

-5 5

y

5

-5

(-5, –1)

(-3, 2)

(1, –3)

D)

x

-5 5

y

5

-5

(-5, –2)

(-3, 1)(-3, 1)

(1, –4)

x

-5 5

y

5

-5

(-5, –2)

(-3, 1)(-3, 1)

(1, –4)

Page80

Completethesquareandthenusetheshiftingtechniquetographthefunction.

33) f(x)=x2+4x

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

A)

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

B)

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

C)

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

D)

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

Page81

34) f(x)=x2–2x–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

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82

Solvetheproblem.

35) Thefollowingnumericalrepresentationforfcomputestheaveragenumberofhoursoftelevisionwatched

perdaybasedonyearofbirthx.

x1975 1980 1983 1988 1990 1992 1995

f(x) 22.5 33.5 43.5 4

Giveanumericalrepresentationforafunctiongthatcomputestheaveragenumberofhoursoftelevision

watchedperdayfortheyearx,wherex=0correspondstothebirthyear1975.Writeanequationthat

showstherelationshipbetweenf(x)andg(x).

A) x05 813151720

g(x) 2 2.5 3 3.5 4 3.5 4

f(x)=g(x–1975)

B) x 75 80 83 88 90 92 95

g(x) 2 2.5 3 3.5 4 3.5 4

f(x)=g(x–1900)

C) x05 813151720

g(x) 2 2.5 3 3.5 4 3.5 4

f(x)=g(x+1975)

D) x05 813151720

g(x) 2 2.5 3 3.5 4 3.5 4

f(x)=g(x)–1975

36) SupposeacoldfrontispassingthroughtheUnitedStatesatnoonwithashapedescribedbythefunction

y=1

24x2,whereeachunitrepresents100miles.St.Louis,Missouriislocatedat(0,0),andthepositive

y–axispointsnorth.

N

W



-10 -5 5 10

10

5

-5

-10

-10 -5 5 10

10

5

-5

-10



E

S

Supposethefrontmovessouth340milesandwest120milesandmaintainsitsshape.Givetheequation

forthenewfrontandplotthenewpositionofthefront.

A) y=1

24(x+1.2)2–3.4

N

W



-10 -5 5 10

10

5

-5

-10

-10 -5 5 10

10

5

-5

-10



E

S

B) y=1

24(x–1.2)2–3.4

N

W



-10 -5 5 10

10

5

-5

-10

-10 -5 5 10

10

5

-5

-10



E

S

Page83

C) y=1

24(x–1.2)2+3.4

N

W



-10 -5 5 10

10

5

-5

-10

-10 -5 5 10

10

5

-5

-10



E

S

D) y=–1

24(x+1.2)2–3.4

N

W



-10 -5 5 10

10

5

-5

-10

-10 -5 5 10

10

5

-5

-10



E

S

2 GraphFunctionsUsingCompressionsandStretches

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

Writetheequationthatresultsinthedesiredtransformation.

1) Thegraphofy=x2,verticallystretchedbyafactorof6

A) y=6x2B) y=–6x2C) y=(x–6)2D) y=6(x–6)x2

2) Thegraphofy=x3,verticallycompressedbyafactorof0.3

A) y=0.3x3B) y=0.3 3xC) y=(x–0.3)3D) y=(x+0.3)3

Supposethepoint(2,4)isonthegraphofy=f(x).Findapointonthegraphofthegivenfunction.

3) y=3f(x)

A) (2,12) B) (6

,

4) C) (2

,

6) D) (5

,

2)

Solvetheproblem.

4) Supposethatthex–interceptsofthegraphofy=f(x)are7 and8.Whatarethex–interceptso

f

y=3f(x)?

A) 7and8B)4and5C)10and11 D) 56and24

Graphthefunctionbystartingwiththegraphofthebasicfunctionandthenusingthetechniquesofshifting,

compressing,stretching,and/orreflecting.

5) f(x)=3x2

x

-5 5

y

5

-5

x

-5 5

y

5

-5

Page84

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

6) f(x)=1

5x2

x

-5 5

y

5

-5

x

-5 5

y

5

-5

Page85

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86

7) f(x)=4x3

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87

8) f(x)=1

3x3

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88

9) f(x)=4x

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89

10) f(x)=1

7x

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

11) f(x)=3|x|

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91

12) f(x)=1

4|x|

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92

13) f(x)=7

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93

14) f(x)=1

5x

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94

15) f(x)=2(x+1)2–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

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95

Usetheaccompanyinggraphofy=f(x)tosketchthegraphoftheindicatedequation.

16) y=2f(x)

x

-10 10

y

10

-10

(-2, 2)

(2, –2)

(-2, 2)

(2, –2)

y = f(x)

x

-10 10

y

10

-10

(-2, 2)

(2, –2)

(-2, 2)

(2, –2)

y = f(x)



x

-10 10

y

10

-10

x

-10 10

y

10

-10

A)

x

-10 10

y

10

-10

(-2, 4)

(2, –4)

(-2, 4)

(2, –4)

x

-10 10

y

10

-10

(-2, 4)

(2, –4)

(-2, 4)

(2, –4)

B)

x

-10 10

y

10

-10

(-2, 1)

(2, –1)

x

-10 10

y

10

-10

(-2, 1)

(2, –1)

C)

x

-10 10

y

10

-10

(-2, 4) (2, 4)

x

-10 10

y

10

-10

(-2, 4) (2, 4)

D)

x

-10 10

y

10

-10

(-2, –4)

(2, 4)

x

-10 10

y

10

-10

(-2, –4)

(2, 4)

Page96

17) y=–1

2f(x)

x

-10 10

y

10

-10

(0, 0)

(3, –4)

(-6, 0)

(-3, –4)

(6, 0)

(3, –4)

y = f(x)

x

-10 10

y

10

-10

(0, 0)

(3, –4)

(-6, 0)

(-3, –4)

(6, 0)

(3, –4)

y = f(x)



x

-10 10

y

10

-10

x

-10 10

y

10

-10

A)

x

-10 10

y

10

-10

(0, 0)(–6, 0)

(-3, 2)

(6, 0)

(3, 2)

x

-10 10

y

10

-10

(0, 0)(–6, 0)

(-3, 2)

(6, 0)

(3, 2)

B)

x

-10 10

y

10

-10

(0, 0)

(-6, 0)

(-3, –2)

(6, 0)

(3, –2)

x

-10 10

y

10

-10

(0, 0)

(-6, 0)

(-3, –2)

(6, 0)

(3, –2)

C)

x

-10 10

y

10

-10

(0, 0)

(-6, 0)

(-3, 4)

(6, 0)

(3, 4)

x

-10 10

y

10

-10

(0, 0)

(-6, 0)

(-3, 4)

(6, 0)

(3, 4)

D)

x

-10 10

y

10

-10

(0, 0)

(1.5, 4)

(-3, 0)

(-1.5, 4)

(3, 0)

x

-10 10

y

10

-10

(0, 0)

(1.5, 4)

(-3, 0)

(-1.5, 4)

(3, 0)

Page97

18) y=–3f(x+5)+3

x

-10 -5 5 10

y

10

5

-5

-10

y = f(x)

x

-10 -5 5 10

y

10

5

-5

-10

y = f(x)



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98

3 GraphFunctionsUsingReflectionsaboutthex–Axisandthey–Axis

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

Matchthecorrectfunctiontothegraph.

1)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A) y=–2x2+1B)y=–2x2C) y=–2x2–1D)y=1–x2

Supposethepoint(2,4)isonthegraphofy=f(x).Findapointonthegraphofthegivenfunction.

2) Thereflectionofthegraphofy=f(x)acrossthex–axis

A) (2,–4) B) (–2,–4) C) (2,4) D) (–2,4)

3) Thereflectionofthegraphofy=f(x)acrossthey–axis

A) (–2,4) B) (2,4) C) (–2,–4) D) (2,–4)

Solvetheproblem.

4) Supposethatthex–interceptsofthegraphofy=f(x)are7 and6.Whatarethex–interceptso

f

y=f(–x)?

A) –7and–6B)7and6C)7and–6D)

–7and6

5) Supposethatthefunctiony=f(x)isdecreasingontheinterval(5

,

7).Whatcanbesaidaboutthegraphof

y=–f(x)?

A) increasingon(5

,

7) B) decreasingon(5

,

7)

C) increasingon(–5

,

–7) D) decreasingon(–5

,

–7)

Findthefunction.

6) Findthefunctionthatisfinallygraphedafterthefollowingtransformationsareappliedtothegraphof

y=|x|.Thegraphisshiftedright3units,stretchedbyafactorof3,shiftedverticallydown2units,and

finallyreflectedacrossthex–axis.

A) y=–(3|x–3|–2) B) y= –3|x–3|–2

C) y=–(3|x+3|–2) D) y=3|–x–3|–2

7) Findthefunctionthatisfinallygraphedafterthefollowingtransformationsareappliedtothegraphof

y=x.Thegraphisshiftedup7units,reflectedaboutthex–axis,andfinallyshiftedleft8units.

A) y=–x+8+7B)y=–x+8–7C)y=-

x–8+7D)y=–x–8–7

8) Findthefunctionthatisfinallygraphedafterthefollowingtransformationsareappliedtothegraphof

y=x.Thegraphisshifteddown6units,reflectedaboutthey–axis,andfinallyshiftedleft8units.

A) y=-

x–8–6B)y=-

x–8+6C)y= – x+8–6D)y=-

x+8+6

Page99

Graphthefunctionbystartingwiththegraphofthebasicfunctionandthenusingthetechniquesofshifting,

compressing,stretching,and/orreflecting.

9) f(x)=–x2

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100

10) f(x)=(–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101

11) f(x)=–x3

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102

12) f(x)=(–x)3

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103

13) f(x)=–x

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104

14) f(x)=–x

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105

15) f(x)=–|x|

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106

16) f(x)=|–x|

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107

17) f(x)=–1

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108

18) f(x)=–(x–5)2–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

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109

19) f(x)=–3(x+1)2–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

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

3.6 MathematicalModels:BuildingFunctions

1 BuildandAnalyzeFunctions

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

Solvetheproblem.

1) Elissawantstosetuparectangulardogruninherbackyard.Shehas42 feetoffencingtoworkwithand

wantstouseitall.Ifthedogrunistobexfeetlong,expresstheareaofthedogrunasafunctionofx.

A) A(x)=21x–x2B) A(x)=22x–x2C) A(x)=23x2–x D) A(x)=20x–x2

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2) Bobwantstofenceinarectangulargardeninhisyard.Hehas76 feetoffencingtoworkwithandwantsto

useitall.Ifthegardenistobexfeetwide,expresstheareaofthegardenasafunctionofx.

A) A(x)=38x–x2B) A(x)=39x–x2C) A(x)=40x2–x D) A(x)=37x–x2

3) Suewantstoputarectangulargardenonherpropertyusing70 metersoffencing.Thereisariverthat

runsthroughherpropertysoshedecidestoincreasethesizeofthegardenbyusingtheriverasonesideof

therectangle.(Fencingisthenneededonlyontheotherthreesides.)Letxrepresentthelengthoftheside

oftherectanglealongtheriver.Expressthegardenʹsareaasafunctionofx.

A) A(x)=35x–1

2x2B) A(x)=36x–2x2C) A(x)=35x2–x D) A(x)=34x–1

4x2

4) Afarmerhas1800yardsoffencingtoenclosearectangulargarden.ExpresstheareaAoftherectangleasa

functionofthewidthxoftherectangle.WhatisthedomainofA?

A) A(x)=–x2+900x;{x|0<x<900} B) A(x)=–x2+1800x;{x|0<x<1800}

C) A(x)=x2+900x;{x|0<x<900} D) A(x)=–x2+900x;{x|0<x<1800}

5) Arectangularsignisbeingdesignedsothatthelengthofitsbase,infeet,is10feetlessthan4timesthe

height,h.Expresstheareaofthesignasafunctionofh.

A) A(h)=–10h+4h2B) A(h)=10h–2h2C) A(h)=–10h2+2h D) A(h)=–10h+h2

6) Arectanglethatisxfeetwideisinscribedinacircleofradius13 feet.Expresstheareaoftherectangleasa

functionofx.

A) A(x)=x 676–x2B) A(x)=x2338–x2

C) A(x)=x(676–x2) D) A(x)=x 507–x

7) Awireoflength8xisbentintotheshapeofasquare.ExpresstheareaAofthesquareasafunctionofx.

A) A(x)=4x2B) A(x)=1

16x2C) A(x)=8x2D) A(x)=2x2

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

8) Arighttrianglehasonevertexonthegraphofy=x2at(x,y),anotherattheorigin,andthethirdonthe

(positive)y–axisat(0,y).ExpresstheareaAofthetriangleasafunctionofx.

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

9) Thefigureshownhereshowsarectangleinscribedinanisoscelesrighttrianglewhosehypotenuseis10

unitslong.ExpresstheareaAoftherectangleintermsofx.

–55

A) A(x)=2x(5–x) B) A(x)=x(5 –x) C) A(x)=2x(x–5) D) A(x)=2x2

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

10) Awire20feetlongistobecutintotwopieces.Onepiecewillbeshapedasasquareandtheotherpiece

willbeshapedasanequilateraltriangle.ExpressthetotalareaAenclosedbythepiecesofwireasa

functionofthelengthxofasideoftheequilateraltriangle.WhatisthedomainofA?

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

11) Afarmerʹssiloistheshapeofacylinderwithahemisphereastheroof.Iftheheightofthesilois94 feet

andtheradiusofthehemisphereisrfeet,expressthevolumeofthesiloasafunctionofr.

A) V(r)=π(94–r)r2+2

3

πr3B) V(r)=94πr2+8

3

πr3

C) V(r)=π(94–r)r3+4

3

πr2D) V(r)=π(94–r)+4

3

πr2

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

12) ThevolumeVofasquare–basedpyramidwithbasesidessandheighthisV=1

3s2h.Iftheheightishalf

ofthelengthofabaseside,expressthevolumeVasafunctionofs.

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

13) Afarmerʹssiloistheshapeofacylinderwithahemisphereastheroof.Iftheradiusofthehemisphereis

10feetandtheheightofthesiloishfeet,expressthevolumeofthesiloasafunctionofh.

A) V(h)=100π(h–10)+2000

3

π B) V(h)=100πh+4000

3

πh2

C) V(h)=100π(h2–10)+5000

3

π D) V(h)=4100π(h–10)+500

7

π

14) Froma34–inchby34–inchpieceofmetal,squaresarecutoutofthefourcornerssothatthesidescanthen

befoldeduptomakeabox.Letxrepresentthelengthofthesidesofthesquares,ininches,thatarecut

out.Expressthevolumeoftheboxasafunctionofx.

A) V(x)=4x3–136x2+1156x B) V(x)=2x3–102x2

C) V(x)=4x3–136x2D) V(x)=2x3–102x2+34x

15) Aboxwithanopentopistobeconstructedfromarectangularpieceofcardboardwithdimensions14

inchesby23inchesbycuttingoutequalsquaresofsidexateachcornerandthenfoldingupthesidesasin

thefigure.ExpressthevolumeVoftheboxasafunctionofx.

23

14

A) V(x)=x(14–2x)(23–2x) B) V(x)=(14 –2x)(23–2x)

C) V(x)=x(14–x)(23–x) D) V(x)=(14 –x)(23–x)

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16) Arectangularboxwithvolume326cubicfeetisbuiltwithasquarebaseandtop.Thecostis$1.50per

squarefootforthetopandthebottomand$2.00persquarefootforthesides.Letxrepresentthelengthof

asideofthebase.Expressthecosttheboxasafunctionofx.

A) C(x)=3x2+2608

xB) C(x)=3x2+1304

xC) C(x)=2x2+2608

xD) C(x)=4x+2608

x2

17) Thepricepandthequantityxsoldofacertainproductobeythedemandequation:

p=–1

8x+100,{x|0≤x≤800}

Whatistherevenuetothenearestdollarwhen700unitsaresold?

A) $8750 B) $131,250 C) $10,000 D) $150,000

18) LetP=(x,y)beapointonthegraphofy=x.ExpressthedistancedfromPtothepoint(1,0)asa

functionofx.

A) d(x)=x2–x+1 B) d(x)=x2+2x+2

C) d(x)=x2+2x+2 D) d(x)=x2–x+1

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

19) Thepricepandx,thequantityofacertainproductsold,obeythedemandequation

p=–1

10x+100,{x|0≤x≤1000}

a) ExpresstherevenueRasafunctionofx.

b) Whatistherevenueif450unitsaresold?

c) Graphtherevenuefunctionusingagraphingutility.

d) Whatquantityxmaximizesrevenue?Whatisthemaximumrevenue?

e) Whatpriceshouldthecompanychargetomaximizerevenue?

20) Twoboatsleaveadockatthesametime.Oneboatisheadeddirectlyeastataconstantspeedof35knots

(nauticalmilesperhour),andtheotherisheadeddirectlysouthataconstantspeedof22knots.Express

thedistancedbetweentheboatsasafunctionofthetimet.

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

21) Arocketisshotstraightupintheairfromthegroundatarateof43 feetpersecond.Therocketistracked

byarangefinderthatis483feetfromthelaunchpad.Letdrepresentthedistancefromtherockettothe

rangefinderandtrepresentthetime,inseconds,sinceʺblastoffʺ.Expressdasafunctionoft.

A) d(t)=4832+(43t)2B) d(t)=4832+(43t)2

C) d(t)=432+(483t)2D) d(t)=483+43t2

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Ch.3 FunctionsandTheirGraphs

AnswerKey

3.1 Functions

1 DetermineWhetheraRelationRepresentsaFunction

2 FindtheValueofaFunction

3 FindtheDomainofaFunctionDefinedbyanEquation

4 FormtheSum,Difference,Product,andQuotientofTwoFunctions

3.2 TheGraphofaFunction

1 IdentifytheGraphofaFunction

2 ObtainInformationfromorabouttheGraphofaFunction

3.3 PropertiesofFunctions

1 DetermineEvenandOddFunctionsfromaGraph

2 IdentifyEvenandOddFunctionsfromtheEquation

3 UseaGraphtoDetermineWhereaFunctionIsIncreasing,Decreasing,orConstant

4 UseaGraphtoLocateLocalMaximaandLocalMinima

5 UseaGraphtoLocatetheAbsoluteMaximumandtheAbsoluteMinimum

6 UseGraphingUtilitytoApproximateLocalMaxima/MinimaandtoDetermineWhereFunctionIsIncrs/Decrs

7 FindtheAverageRateofChangeofaFunction

3.4 LibraryofFunctions;Piecewise–definedFunctions

1 GraphtheFunctionsListedintheLibraryofFunctions

2 GraphPiecewise–definedFunctions

3.5 GraphingTechniques:Transformations

1 GraphFunctionsUsingVerticalandHorizontalShifts

2 GraphFunctionsUsingCompressionsandStretches

3 GraphFunctionsUsingReflectionsaboutthex–Axisandthey–Axis

3.6 MathematicalModels:BuildingFunctions

1 BuildandAnalyzeFunctions

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