Chapter 3 If a rock falls from a height of 40 meters on Earth

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→25

10 →50

15 →75

20 →100

A) function

domain:{5,10,15,20}

range:{25,50,75,100}

B) function

domain:{25,50,75,100}

range:{5,10,15,20}

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) {(–1

,

–7),(0

,

5),(5

,

0),(8

,

–2)}

A) function

domain:{–1,0,5,8}

range:{–7,5,0,–2}

B) function

domain:{–7,5,0,–2}

range:{–1,0,5,8}

C) notafunction

5) {(41

,

–3),(5

,

–2),(5

,

0),(9

,

2),(21

,

4)}

A) function

domain:{41,9,5,21}

range:{–3,–2,0,2,4}

B) function

domain:{–3,–2,0,2,4}

range:{41,9,5,21}

C) notafunction

6) {(–4

,

21),(–3

,

14),(0,5),(3

,

14),(5

,

30)}

A) function

domain:{–4,–3,0,3,5}

range:{21,14,5,30}

B) function

domain:{21,14,5,30}

range:{–4,–3,0,3,5}

C) notafunction

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7) {(1.55,5.15),(1.555,–5.1),(3

7,0),(0.43,–1)}

A) function

domain:{1.55,1.555,3

7,0.43}

range:{5.15,–5.1,0,–1}

B) function

domain:{5.15,–5.1,0,–1}

range:{1.55,1.555,3

7,0.43}

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=8–x2

A) function B) notafunction

12) y=±1–2x

A) function B) notafunction

13) x=y2

A) function B) notafunction

14) y2+x=9

A) function B) notafunction

15) y=6x2–5x+8

A) function B) notafunction

16) y=3x–1

x+1

A) function B) notafunction

17) x2–5y2=1

A) function B) notafunction

18) x+6y=2

A) function B) notafunction

19) 4x+x2+79=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(–1)whenf(x)=x2+2x+5.

A) 4 B) –6C)

–2D)8

2) Findf(2)whenf(x)=x2–4

x+1

.

A) 0 B) 8

3C) 4

3D) –2

3) Findf(–9)whenf(x)=|x|–6.

A) 3 B) –15 C) 15 D) –3

4) Findf(5)whenf(x)=x2+7x.

A) 2 15 B) 74 C) 2 14 D) 4 2

5) Findf(–x)whenf(x)=3x2–4x–3.

A) 3x2+4x–3B)

–3x2+4x+3C)3x

2+4x+3D)

–3x2+4x–3

6) Findf(–x)whenf(x)=x

x2+1

.

A) –x

x2+1

B) –x

x2–1

C) x

–x2+1

D) –x

–x2+1

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

A) 3x2–2x–1B)

–3x2–2x+1C)

–3x2–2x–1D)3x

2–2x+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+2.

A) 3x2–10x+9B)

–10x2+3x+9C)3x

2–10x+1D)3x

2+2x+1

10) Findf(x+1)whenf(x)=x2–2

x–3.

A) x2+2x–1

x–2B) x2+2x+3

x–2C) x2+2x–1

x+4D) x2–1

x–2

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

A) –12x2+6x+2B)

–6x2+6x+2C)

–6x2+6x+4D)

–12x2+6x+4

12) Findf(2x)whenf(x)=4x2+7x.

A) 16x2+14x B) 2 4x2+7x C) 8x2+14x D) 8x2+28x

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13) Findf(x+h)whenf(x)=–3x2–4x–2.

A) –3x2–6xh–3h2–4x–4h–2B)

–3x2–3h2–4x–4h–2

C) –3x2–3h2–10x–10h–2D)

–3x2–3xh–3h2–4x–4h–2

14) Findf(x+h)whenf(x)=–4x+7

5x–2.

A) –4x–4h+7

5x+5h–2B) –4x–4h+7

5x–2C) –4x+3h

5x+3h D) –4x+7h

5x–2h

Solvetheproblem.

15) Iff(x)=7x3+7x2–x+Candf(–2)=1,whatisthevalueofC?

A) C=27 B) C=3C)C= –85 D) C= –29

16) Iff(x)=x–B

x–A,f(–9)=0,andf(8)isundefined,whatarethevaluesofAandB?

A) A=8

,

B=–9B)A=–9

,

B=8C)A= –8

,

B=9D)A=9

,

B= –8

17) Iff(x)=x–2A

–6x+4

andf(–6)=–2,whatisthevalueofA?

A) A=37 B) A=–37 C) A= –43 D) A=43

18) 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.

Whatistheheightoftherockwhenx=1.8seconds?Roundtothenearesthundredth,ifnecessary.

A) 24.12m B) 55.88 m C) 31.18 m D) 24.45 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)=0.25t+1,fort>10.Findtheapproximatenumberoffishthatcanbecaughtifyoufish

for10minutes.

A) About3fish B) About8 fish C) About12 fish D) About14 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47feet.

A) 80

33

atm B) 47

33

atm C) 14

33

atm D) 16

11

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20°C.

A) 68°F B) 104°F C) 140°F D) 176°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–8

A) allrealnumbers B) {x|x≥8} C) {x|x≠0} D) {x|x>0}

2) f(x)=x2+6

A) allrealnumbers B) {x|x≥–6} C) {x|x> –6} D) {x|x≠–6}

3) f(x)=x2

x2+7

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

4) g(x)=x

x2–1

A) {x|x≠–1

,

1} B) {x|x≠0} C) {x|x>1} D) allrealnumbers

5) h(x)=x–1

x3–9x

A) {x|x≠–3

,

0,3} B) {x|x≠0} C) {x|x≠1} D) allrealnumbers

6) f(x)=14–x

A) {x|x≤14} B) {x|x≠14} C) {x|x≤14} D) {x|x≠14}

7) x

x–7

A) {x|x>7} B) {x|x≥7} C) {x|x≠7} 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)=2–7x;g(x)=–5x+7

Findf+g.

A) (f+g)(x)=–12x+9;allrealnumbers B) (f+g)(x)=–5x+2;{x|x≠2

5}

C) (f+g)(x)=–3x;allrealnumbers D) (f+g)(x)=–2x+9;{x|x≠–9

2}

2) f(x)=8x–2;g(x)=4x–8

Findf–g.

A) (f–g)(x)=4x+6;allrealnumbers B) (f–g)(x)=4x–10;{x|x≠5

2}

C) (f–g)(x)=12x–10;{x|x≠1} D) (f–g)(x)= –4x–6;allrealnumbers

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3) f(x)=2x+2;g(x)=5x–1

Findf·g.

A) (f·g)(x)=10x2+8x–2;allrealnumbers B) (f·g)(x)=10x2+9x–2;{x|x≠–2}

C) (f·g)(x)=7x2+8x+1;allrealnumbers D) (f·g)(x)=10x2–2;{x|x≠–2}

4) f(x)=5x+1;g(x)=3x–5

Findf

g.

A) f

g(x)=5x+1

3x–5; x|x≠5

3B) f

g(x)=5x+1

3x–5; x|x≠–1

5

C) f

g(x)=3x–5

5x+1; x|x≠5

3D) f

g(x)=3x–5

5x+1; x|x≠–1

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–2;g(x)=9x2

Findf+g.

A) (f+g)(x)=9x2+x–2;allrealnumbers B) (f+g)(x)=9x2–x+2;allrealnumbers

C) (f+g)(x)=9x2+x–2;{x|x≠2} D) (f+g)(x)=–9x2+x–2;allrealnumbers

7) f(x)=2x3–1;g(x)=5x2–1

Findf·g.

A) (f·g)(x)=10x5–2x3–5x2+1;allrealnumbers

B) (f·g)(x)=10x6–2x3–5x2+1;allrealnumbers

C) (f·g)(x)=10x5–2x3–5x2+1;{x|x≠0}

D) (f·g)(x)=2x3+5x2+1;allrealnumbers

8) f(x)=x;g(x)=6x–1

Findf

g.

A) f

g(x)=x

6x–1; x|x≥0,x≠1

6B) f

g(x)=x

6x–1; x|x≠1

6

C) f

g(x)=x

6x–1;{x|x≠0} D) f

g(x)=6x–1

x;{x|x≥0}

9) f(x)=7–x;g(x)=x–3

Findf·g.

A) (f·g)(x)=(7–x)(x–3);{x|3≤x≤7} B) (f·g)(x)=(7–x)(x–3);{x|x≥0}

C) (f·g)(x)=(7–x)(x–3);{x|x≠3,x≠7} D) (f·g)(x)=–x2–21;{x|x≠21}

Page6

10) f(x)=9x+7

3x–8;g(x)=7x

3x–8

Findf–g.

A) (f–g)(x)=2x+7

3x–8; x|x≠8

3B) (f–g)(x)=16x–7

3x–8; x|x≠8

3

C) (f–g)(x)=2x+7

3x–8; x|x≠8

3,x≠–7

2D) (f–g)(x)=2x+7

3x–8;{x|x≠0}

11) f(x)=x+11;g(x)=3

x

Findf·g.

A) (f·g)(x)=3x+11

x;{x|x≥–11,x≠0} B) (f·g)(x)=3x+33

x;{x|x≥–11,x≠0}

C) (f·g)(x)=3x+33

x;{x|x≥–11,x≠0} D) (f·g)(x)=14

x;{x|x≠0}

Solvetheproblem.

12) Givenf(x)=1

x

and(f

g)(x)=x+3

x2–2x

,findthefunctiong.

A) g(x)=x–2

x+3B) g(x)=x+3

x–2C) g(x)=x+2

x–3D) g(x)=x–3

x+2

13) Find(f+g)(–2)whenf(x)=x+2andg(x)=x–1.

A) –3B)

–7C)

–1D)

–5

14) Find(f–g)(4)whenf(x)=4x2+5andg(x)=x–1.

A) 66 B) –73 C) 64 D) 74

15) Find(fg)(4)whenf(x)=x–1andg(x)=–2x2+12x–5.

A) 33 B) –185 C) 55 D) 177

16) Findf

g(–3)whenf(x)=2x–1andg(x)=4x2+14x+2.

A) 7

4B) –1C)

4

5D) 0

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

h,h≠0,forthefunction.

17) f(x)=6x–8

A) 6 B) 6+–16

hC) 6+12(x–8)

hD) 0

18) f(x)=4x2

A) 4(2x+h) B) 8

h

+x+4h C) 4(2x2+2xh+h2)

hD) 4

19) f(x)=3

A) 0 B) 1 C) 1+6

hD) 3

Page7

20) f(x)=1

4x

A) –1

4x(x+h) B) –1

x(x+h) C) 1

4x D) 0

21) f(x)=x2+9x–1

A) 2x+h+9B)

2x2+2x+2xh+h2+h–2

h

C) 2x+h–1D)1

Solvetheproblem.

22) ExpressthegrosssalaryGofapersonwhoearns$16 perhourasafunctionofthenumberxofhours

worked.

A) G(x)=16x B) G(x)=16 +x C) G(x)=16

xD) G(x)=16x2

23)

J

acey,acommissionedsalesperson,earns$340 basepayplus$36 peritemsold.ExpressJaceyʹsgross

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

A) G(x)=36x+340 B) G(x)=340x+36 C) G(x)=36(x+340) D) G(x)=340(x+36)

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

incomeinyearx.DetermineafunctionCthatrepresentstotalclothingexpendituresinyearx.

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

P(x)

25) Aretailstorebuys120VCRsfromadistributoratacostof$160 eachplusanoverheadchargeof$30 per

order.Theretailmarkupis30%onthetotalpricepaid.FindtheprofitonthesaleofoneVCR.

A) $48.08 B) $4808.00 C) $48.00 D) $47.93

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)=70x+4660.

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

R(x)=80x,

butthatnomorethan747unitscanbesoldatthatprice.Findandinterpret(R–C)(747).

A) $2810profit,incomeexceedscos

t

Itisworthittodevelopproduct.

B) –$2810 loss,costexceedsincome

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

C) $116,710profit,incomeexceedscos

t

Itisworthittodevelopproduct.

D) $1213 profit,incomeexceedscos

t

Itisworthittodevelopproduct.

28) Thefunctionf(t)=–0.15t2+0.53t+30.1modelstheU.S.populationinmillions,ages65andolder,wheret

representsyearsafter1990.Thefunctiong(t)=0.51t2+12.04t+105.9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(10).

A) Costperpersoninthousandsofdollars.$13.59 thousand

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

C) Costperpersoninthousandsofdollars.$0.07 thousand

D) Costperpersoninthousandsofdollars.$8.44 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≤–1orx≥1}

range:allrealnumbers

intercepts:(–1,0),(1,0)

symmetry:x–axis,y–axis,origin

B) function

domain:allrealnumbers

range:{y|y≤–1ory≥1}

intercepts:(–1,0),(1,0)

symmetry:y–axis

C) function

domain:{x|–1≤x≤1}

range:allrealnumbers

intercepts:(–1,0),(1,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:(–3,0),(0,3),(1,0)

symmetry:none

B) function

domain:{x|x≤4}

range:allrealnumbers

intercepts:(–3,0),(0,3),(1,0)

symmetry:y–axis

C) function

domain:allrealnumbers

range:{y|y≤4}

intercepts:(0,–3),(3,0),(0,1)

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|–4≤x≤4}

range:{y|–4≤y≤4}

intercepts:(–4,0),(0,–4),(0,4),(4,0)

symmetry:x–axis,y–axis,origin

B) function

domain:{x|–4≤x≤4}

range:{y|–4≤y≤4}

intercepts:(–4,0),(0,–4),(0,4),(4,0)

symmetry:x–axis,y–axis

C) function

domain:{x|–4≤x≤4}

range:{y|–4≤y≤4}

intercepts:(–4,0),(0,–4),(0,0),(0,4),(4,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=2ory=6}

intercept:(0,6)

symmetry:none

B) function

domain:{x|x=2orx=6}

range:allrealnumbers

intercept:(6,0)

symmetry:x–axis

C) function

domain:allrealnumbers

range:allrealnumbers

intercept:(0,6)

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(20).

50

–50 50

–50

A) –40 B) 20 C) 0 D) 30

2) Isf(20)positiveornegative?

25

–25 25

–25

A) positive B) negative

Page14

3) Isf(15)positiveornegative?

25

–25 25

–25

A) positive B) negative

4) Forwhatnumbersxisf(x)=0?

5

–55

–5

A) –3

,

3.5

,

5B)(

–5

,

–3),(3.5

,

5) C) (–3

,

3.5) D) –3

Page15

5) Forwhatnumbersxisf(x)>0?

100

–100 100

–100

A) [–100

,

–60),(70

,

100) B) (–60

,

70)

C) (–60

,

∞)D)(

–∞–60)

6) Forwhatnumbersxisf(x)

<

0?

10

–10 10

–10

A) (–6

,

7) B) [–10

,

–6),(7

,

10) C) (–6

,

∞)D)(

–∞

,

–6)

Page16

7) Whatisthedomainoff?

25

–25 25

–25

A) {x|–25≤x≤25} B) {x|–20 ≤x≤27.5} C) allrealnumbers D) {x|x≥0}

8) Whatarethex–intercepts?

20

–20 20

–20

A) –12

,

14

,

20 B) –20

,

–12

,

14

,

20 C) –12

,

14 D) –12

Page17

9) Whatisthey–intercept?

10

–10 10

–10

A) –6 B) 7 C) 10 D) –8

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=2intersectthegraph?

10

–10 10

–10

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

t

12) Forwhichofthefollowingvaluesofxdoesf(x)=10?

25

–25 25

–25

A) 20 B) 35 C) 25 D) 10

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

13) Giventhefunctionf(x)=–7x2+14x–4,isthepoint(1,3)onthegraphoff?

A) Yes B) No

14) Giventhefunctionf(x)=4x2–8x+4,isthepoint(2,12)onthegraphoff?

A) Yes B) No

15) Giventhefunctionf(x)=–4x2+8x+8,ifx=1,whatisf(x)?Whatpointisonthegraphoff?

A) 12;(1

,

12) B) 12;(12

,

1) C) –4;(1

,

–4) D) –4;(–4

,

1)

16) Giventhefunctionf(x)=7x2–14x+2,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+3x–28,listthex–intercepts,ifany,ofthegraphoff.

A) (–7

,

0),(4

,

0) B) (7

,

0),(4

,

0) C) (–7

,

0),(1,0) D) (7

,

0),(–4

,

0)

Page19

18) Giventhefunctionf(x)=–6x2+12x–9,listthey–intercept,ifthereisone,ofthegraphoff.

A) –9B)

–21 C) –3D)

–27

19) Giventhefunctionf(x)=x2–7

x+3,isthepoint(–1,–3)onthegraphoff?

A) Yes B) No

20) Giventhefunctionf(x)=x2–5

x+3,isthepoint(1,3

2)onthegraphoff?

A) Yes B) No

21) Giventhefunctionf(x)=x2–3

x–3,ifx=2,whatisf(x)?Whatpointisonthegraphoff?

A) –1;(2

,

–1) B) –1;(–1

,

2) C) –7;(2

,

–7) D) –7;(–7

,

2)

22) Giventhefunctionf(x)=x2+7

x–8,whatisthedomainoff?

A) {x|x≠8} B) {x|x≠–8} C) {x|x≠7} D) {x|x≠7

8}

23) Giventhefunctionf(x)=x2+9

x–6,listthex–intercepts,ifany,ofthegraphoff.

A) (9

,

0),(–9

,

0) B) (6

,

0) C) (–3

,

0) D) none

24) Giventhefunctionf(x)=x2+4

x–8,listthey–intercept,ifthereisone,ofthegraphoff.

A) (0,–1

2)B)(

–1

2,0) C) (0,8) D) (0,–4)

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2blocksin10 minutesata

constantspeed,andrealizesthatheforgothiswalletathome.SoMichaelrunsbackin4minutes.Athome,

ittakeshim4minutestofindhiswalletandclosethedoor.Michaelwalks2blocksin10minutesandthen

decidestojogtothemall.Ittakeshim4minutestogettothemallwhichis2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650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+1300

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) 4.7cm B) 5.9cm C) 3.9 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

0.62t+1.612 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) 2.6hours B) 4.1hours C) 3.4 hours D) 4.9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)=–9x2–8

A) even B) odd C) neither

4) f(x)=2x3+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) 33x2+5

A) even B) odd C) neither

8) f(x)=1

x2

A) even B) odd C) neither

9) f(x)=x

x2–2

A) even B) odd C) neither

Page26

10) f(x)=–x3

6x2–5

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) (–4

,

–2)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

A) decreasing B) increasing C) constant

2) (–5

2,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,3)

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) (–1

,

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) (1

,

∞)

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) (–2

,

∞)

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

,

0)

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) (–5

,

–4)

x

-5 5

y

5

-5

(-5, –3) (-4, –3)

(0.5, 1.5) (3.5, 1.5)

(6, -2.2)

x

-5 5

y

5

-5

(-5, –3) (-4, –3)

(0.5, 1.5) (3.5, 1.5)

(6, -2.2)

A) constant B) increasing C) decreasing

11) (–6

,

–2.5)

x

-5 5

y

5

-5

(-6, 2)

(-2.5, 0)

(-1, –3) (0, –3)

(2, 0)

(5, –3)

x

-5 5

y

5

-5

(-6, 2)

(-2.5, 0)

(-1, –3) (0, –3)

(2, 0)

(5, –3)

A) decreasing B) increasing C) constant

Page30

12) (–∞

,

–8)

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3

B) fhasalocalmaximumatx=–3 and3;thelocalmaximumis0

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

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=–3and3;thelocalminimumis0

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

C) fhasalocalminimumatx=–3;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80 feetpersecondfromaninitialheighto

f

4feetisgivenasafunctionoftimet(inseconds)bys(t)=–16t2+80t+4.Whatisthemaximumheight?

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

x

y

x

y

A) 104ft B) 116.5 ft C) 100.25 ft D) –74.75 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–3x +3,(–2,2)

A) localmaximumat(–1

,

5)

localminimumat(1,1)

increasingon(–2,–1)and(1,2)

decreasingon(–1,1)

B) localmaximumat(1

,

1)

localminimumat(–1,5)

increasingon(–2,–1)and(1,2)

decreasingon(–1,1)

C) localmaximumat(–1

,

5)

localminimumat(1,1)

increasingon(–1,1)

decreasingon(–2,–1)and(1,2)

D) localmaximumat(1

,

1)

localminimumat(–1,5)

increasingon(–2,–1)

decreasingon(–1,1)

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+54x+68,withPbeingprofitsandxthenumberofhotdogssold.Howmanyhotdogsmusthe

selltoearnthemostprofit?

A) 27hotdogs B) 41hotdogs C) 28 hotdogs D) 20hotdogs

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

c(x)=3x2–198x+69,whereciscostandxisthenumberofwatchesrepaired.Howmanywatchesmust

herepairtohavethelowestcost?

A) 33watches B) 30watches C) 69 watches D) 34watches

13) Johnownsahotdogstand.HisprofitisrepresentedbytheequationP(x)=–x2+12x+44,withPbeing

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

A) $80 B) $68 C) $104 D) $36

Page39

14) Arockfallsfromatowerthatis102.9 mhigh.Asitisfalling,itsheightisgivenbytheformula

h(t)=102.9–4.9t2.Howmanysecondswillittakefortherocktohittheground(h=0)?Roundtothe

nearesttenth.

A) 4.6sec B) 10.1 sec C) 2200 sec D) 21.2 sec

15) Aprojectileisthrownupwardsothatitsdistanceabovethegroundaftertsecondsish(t)=–16t2+540t.

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

A) 17sec B) 9sec C) 27 sec D) 36sec

16) Arockfallsfromatowerthatis368fthigh.Asitisfalling,itsheightisgivenbytheformula

h(t)=368–16t2.Howmanysecondswillittakefortherocktohittheground(h=0)?Roundtothenearest

tenth.

A) 4.8sec B) 19.2 sec C) 8464 sec D) 23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)=–3x

A) –3B)

–4C)

–3

x–1D) 0

2) f(x)=x2–2x

A) x –1B)x

+1C)1 D)

x2–2x–1

x–1

3) f(x)=3

x+2

A) –1

x+2B) 1

x+2C) 3

(x–1)(x+2) D) 3

x(x+2)

4) f(x)=x+80

A) x+80–9

x–1B) x+80+9

x+1C) x+80–9

x+1D) x+80+9

x–1

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

5) f(x)=4x–8;from1to2

A) 4 B) 8 C) –4D)

–8

6) f(x)=x2+4x;from6to8

A) 18 B) 48 C) 9

2D) 12

7) f(x)=8x3–2x2+2;from2to4

A) 212 B) 241 C) 106 D) 241

2

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)=x2–2x

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

16) f(x)=5

x+4

A) y=–1

6x+7

6B) y=1

6x+5

6C) y=5

6x+1

6D) y=1

6x+7

5

17) f(x)=x+63

A) y=(65–8)x–65+16 B) y=(–65+8)x+65–16

C) y=(65

–8)x+65–16 D) y=(–65–8)x–65+16

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 109

June 88

July 100

August 96

September 112

October 92

November 86

December 66

A) $8.00permonth B) –$8.00 permonth

C) $12.00permonth D) –$12.00 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 $1910

1994 $2440

1995 $2480

1996 $2830

1997 $3010

1998 $3130

A) $265peryear B) $530 peryear C) $325 peryear D) $285 peryear

20) Adeepseadivingbellisbeingloweredataconstantrate.After10 minutes,thebellisatadepthof600 ft.

After40minutesthebellisatadepthof1800ft.Whatistheaveragerateofloweringperminute?Round

tothenearesthundredthisneeded.

A) 40.0ftperminute B) 0.03 ftperminute C) 30.0 ftperminute D) 45.0 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)=–5

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+2if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

–9ifx=–2

–x+6if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, 3)

(-2, –9)

(-2, 8)

x

-10 -5 5 10

y

10

5

-5

-10

(-8, –3)

(-2, 3)

(-2, –9)

(-2, 8)

B)

x

-10 -5 5 10

y

10

5

-5

-10

(-8, –3)

(-2, 3)

(-2, –9)

(-2, 8)

x

-10 -5 5 10

y

10

5

-5

-10

(-8, –3)

(-2, 3)

(-2, –9)

(-2, 8)

C)

x

-10 -5 5 10

y

10

5

-5

-10

(-8, –2)

(-2, 4)

(-2, –9)

(-2, 8)

x

-10 -5 5 10

y

10

5

-5

-10

(-8, –2)

(-2, 4)

(-2, –9)

(-2, 8)

D)

x

-10 -5 5 10

y

10

5

-5

-10

(-8, –2)

(-2, 4)

(-2, –9)

(-2, 8)

x

-10 -5 5 10

y

10

5

-5

-10

(-8, –2)

(-2, 4)

(-2, –9)

(-2, 8)

5)

f(x)=

1if0≤x<3

|x| if3≤x<7

xif7≤x≤11

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

(0, 1) (3, 1)

(3, 3)

(7, 7)

(7, 2.6) (11, 3.3)

x

–10 -5 5 10 15

y

10

5

-5

-10

(0, 1) (3, 1)

(3, 3)

(7, 7)

(7, 2.6) (11, 3.3)

B)

x

-10 -5 5 10 15

y

10

5

-5

-10

(0, 1) (3, 1)

(3, 3)

(7, 7)

(7, 2.6) (11, 3.3)

x

-10 -5 5 10 15

y

10

5

-5

-10

(0, 1) (3, 1)

(3, 3)

(7, 7)

(7, 2.6) (11, 3.3)

C)

x

–10 -5 5 10 15

y

10

5

-5

-10

(0, –1) (3, –1)

(3, 3)

(7, 7)

(7, 2.6) (11, 3.3)

x

–10 -5 5 10 15

y

10

5

-5

-10

(0, –1) (3, –1)

(3, 3)

(7, 7)

(7, 2.6) (11, 3.3)

D)

x

-10 -5 5 10 15

y

10

5

-5

-10

(0, –1) (3, –1)

(3, 3)

(7, 7)

(7, 2.6) (11, 3.3)

x

-10 -5 5 10 15

y

10

5

-5

-10

(0, –1) (3, –1)

(3, 3)

(7, 7)

(7, 2.6) (11, 3.3)

Findthedomainofthefunction.

6)

f(x)=5x ifx≠0

5ifx=0

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

7)

f(x)=

1if–6≤x<–2

|x| if–2≤x<6

3xif6≤x≤22

A) {x|–6≤x≤22} B) {x|x≥–6}

C) {x|–6≤x

<

6or6

<

x≤22} D) {x|6 ≤x≤22}

Page56

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

8)

f(x)=–7x+8ifx<1

8x–7ifx≥1

A) (0,8) B) (0,8),(8

7,0),(7

8,0)

C) (0,–7) D) (0,–7),(8

7,0),(7

8,0)

9)

f(x)=

1if–5≤x<–3

|x| if–3≤x<5

xif5≤x≤30

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

5ifx=0

x

-10 -5 5

y

10

5

-5

-10

(0, 5)

x

-10 -5 5

y

10

5

-5

-10

(0, 5)

A) (–∞

,

0)or(0,∞)B)(

–∞

,

∞)

C) (–10,10) D) (–∞

,

0)or{0}or(0,∞)

Page57

11)

f(x)=

4if–5≤x<–2

|x| if–2≤x<8

3xif8≤x≤13

x

–10 -5 5 10 15

y

10

5

-5

-10

(-5, 4) (-2, 4)

(-2, 2)

(8, 8)

(8, 2)

(13, 2.4)

x

–10 -5 5 10 15

y

10

5

-5

-10

(-5, 4) (-2, 4)

(-2, 2)

(8, 8)

(8, 2)

(13, 2.4)

A) [0,8) B) [0,∞) C) [0,313] D) [0,8]

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(4x),findf(1.6).

A) 6 B) 7 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4unitsdownward

A) y=x2–4B)y=x2+4C)y=x2

4D) y=4x2

4) Thegraphofy=x

,

shifted8unitstotheright

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

5) Thegraphofy=x

,

shifted5unitsupward

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

6) Thegraphofy=x,shifted9unitstotheright

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

7) Thegraphofy=x,shifted9unitstotheleft

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

Page62

8) Thegraphofy=x,shifted7unitsupward

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

9) Thegraphofy=x,shifted2unitsdownward

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

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+4)

A) (–2

,

4) B) (6

,

4) C) (2,0) D) (2,8)

11) f(x)+8

A) (2,12) B) (2,–8) C) (10

,

4) D) (–6

,

4)

Solvetheproblem.

12) Supposethatthex–interceptsofthegraphofy=f(x)are2 and3.Whatarethex–interceptso

f

y=f(x+7)?

A) –5and–4B)9and10 C) 14 and21 D) 2and10

13) Supposethatthex–interceptsofthegraphofy=f(x)are9 and2.Whatarethex–interceptso

f

y=f(x–7)?

A) 16and9B)2and–5C)63and14 D) 9and–5

14) Supposethatthefunctiony=f(x)isincreasingontheinterval(2

,

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

y=f(x+3)increasing?

A) (–1

,

4) B) (5

,

10) C) (6

,

21) D) (2

,

7)

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

,

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

y=f(x–6)increasing?

A) (10

,

14) B) (–2

,

2) C) (24 ,48) D) (4

,

8)

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+3

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+4)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–2)2+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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+5)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–6)3–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69

22) f(x)=x–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70

23) 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71

24) f(x)=x–6–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72

25) f(x)=x+5+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73

26) f(x)=|x|–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74

27) 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75

28) f(x)=|x–4|–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

29) f(x)=1

x

–1

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–1

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+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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–10x

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–3x–9

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

27x2,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

27(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

27(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

27(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

27(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5

A) y=5x2B) y=–5x2C) y=(x–5)2D) y=5(x–5)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8 and5.Whatarethex–interceptso

f

y=7f(x)?

A) 8and5B)1and–2C)15and12 D) 40and35

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)=7x2

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

2x2

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)=7x3

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

7x3

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)=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

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

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

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90

11) f(x)=2|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

2|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)=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93

14) f(x)=1

2x

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)=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

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=–1

4f(x+3)+5

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3 and5.Whatarethex–interceptso

f

y=f(–x)?

A) –3and–5B)3and5C)3and–5D)

–3and5

5) Supposethatthefunctiony=f(x)isdecreasingontheinterval(8

,

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

y=–f(x)?

A) increasingon(8

,

5) B) decreasingon(8

,

5)

C) increasingon(–8

,

–5) D) decreasingon(–8

,

–5)

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9units,reflectedaboutthex–axis,andfinallyshiftedleft7units.

A) y=–x+7+9B)y=–x+7–9C)y=-

x–7+9D)y=–x–7–9

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5units,reflectedaboutthex–axis,andfinallyshiftedleft3units.

A) y=–

,

x+3–5B)y=–

,

x+3+5C)y=-

x–3–5D)y= –

,

x–3+5

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+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109

19) 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

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48 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)=24x–x2B) A(x)=25x–x2C) A(x)=26x2–x D) A(x)=23x–x2

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2) Bobwantstofenceinarectangulargardeninhisyard.Hehas60 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)=30x–x2B) A(x)=31x–x2C) A(x)=32x2–x D) A(x)=29x–x2

3) Suewantstoputarectangulargardenonherpropertyusing68 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)=34x–1

2x2B) A(x)=35x–2x2C) A(x)=34x2–x D) A(x)=33x–1

4x2

4) Afarmerhas1600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+800x;{x|0<x<800} B) A(x)=–x2+1600x;{x|0<x<1600}

C) A(x)=x2+800x;{x|0<x<800} D) A(x)=–x2+800x;{x|0<x<1600}

5) Arectangularsignisbeingdesignedsothatthelengthofitsbase,infeet,is12feetlessthan4timesthe

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

A) A(h)=–12h+4h2B) A(h)=12h–2h2C) A(h)=–12h2+2h D) A(h)=–12h+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9xisbentintotheshapeofasquare.ExpresstheareaAofthesquareasafunctionofx.

A) A(x)=81

16x2B) A(x)=1

16x2C) A(x)=81

8x2D) A(x)=9

4x2

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8

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

–44

A) A(x)=2x(4–x) B) A(x)=x(4 –x) C) A(x)=2x(x–4) 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77 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(77–r)r2+2

3

πr3B) V(r)=77πr2+8

3

πr3

C) V(r)=π(77–r)r3+4

3

πr2D) V(r)=π(77–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50–inchby50–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–200x2+2500x B) V(x)=2x3–150x2

C) V(x)=4x3–200x2D) V(x)=2x3–150x2+50x

15) Aboxwithanopentopistobeconstructedfromarectangularpieceofcardboardwithdimensions10

inchesby30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.

30

10

A) V(x)=x(10–2x)(30–2x) B) V(x)=(10 –2x)(30–2x)

C) V(x)=x(10–x)(30–x) D) V(x)=(10 –x)(30–x)

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16) Arectangularboxwithvolume374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+2992

xB) C(x)=3x2+1496

xC) C(x)=2x2+2992

xD) C(x)=4x+2992

x2

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

p=–1

8x+400,{x|0≤x≤800}

Whatistherevenuetothenearestdollarwhen500unitsaresold?

A) $168,750 B) $231,250 C) $30,000 D) $280,000

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70 feetpersecond.Therocketistracked

byarangefinderthatis474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)=4742+(70t)2B) d(t)=4742+(70t)2

C) d(t)=702+(474t)2D) d(t)=474+70t2

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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

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3.3 PropertiesofFunctions

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

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

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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

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3.5 GraphingTechniques:Transformations

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

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

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

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3.6 MathematicalModels:BuildingFunctions

1 BuildandAnalyzeFunctions

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