Algebra Quiz

Thereare30problems.

Problems#1–12areMultipleChoice.

Problems#13–21areShortAnswer.(Worknotrequiredtobeshown) Problems#22–30areShortAnswerwithworkrequiredtobeshown.

MULTIPLECHOICE

1. Determinethedomainand rangeof thepiecewise function.                                                               1.  C

4

2

-4     -2                2      4

-2

-4

A.     Domain[–3,1];Range[–1,3] B.   Domain[–1,1];Range[0,1] C.    Domain[–1,3];Range[–3,1]

D.     Domain[1/2,3/2];Range[0,1]

2.Solve:

x+ 35=x− 7

2. B

A.     1,14

B.     14

C.     1

D.     Nosolution

3. Determinetheinterval(s) on which the function is decreasing.                                                           3. C

A.     (–1,3) B.   (–2,2)

C.     (–∞,–1)and (3,∞)

D.     (–2.5,1)and(4.5,∞)

4.Determinewhetherthegraphof

y= 3x

issymmetricwithrespecttotheorigin,

the x-axis, or the y-axis.                                                                                                            4. C

A.     notsymmetricwithrespecttothex-axis,notsymmetricwithrespecttothey-axis,and notsymmetricwithrespecttotheorigin

B.      symmetricwithrespecttothex-axisonly C.      symmetricwithrespecttothey-axisonly D.     symmetricwithrespecttotheoriginonly

5.Solve,andexpresstheanswerinintervalnotation:      5− 4x

≥ 11.                         5.A

A.     (–∞,–3/2]∪[4,∞)

B.     (–∞,  4] ∪[–3/2,∞)

C.     [–3/2,4] D. [–3/2,∞)

6. Which of the followingrepresents thegraph of  2x+9y=18 ?                                                        6. A

A.                                                                       B.

C.                                                                        D.

7.Writeaslope-interceptequationforalineparalleltothelinex+3y=8whichpassesthrough thepoint(– 4, 5).   7.C

A.      y=1x+ 5

3

B.      y=− 3x− 7

C.      y=− 1x+ 11

3       3

D.      y=− 1x+ 5

3

8. Which of the followingbest describes thegraph?                                                                          8.D

A.   It isnotthegraphof afunction. B.   It isaparabolicgraph.

C.   It isthegraphofaone-to-onefunction.

D.   It isthegraphof afunctionbutnotone-to-one.

9. Expressasa single logarithm:   logx –  3 logy  +  log1                                                          9. B

3

x+1 

A.     log

  y  

       

x

B.      log  3

    

C.      log( x− 3y+1)

   x    

D.     log

3 y+ 1 

10. Which of the functionscorresponds to thegraph?                                                                      10. A

A.   f( x ) = ex+ 2

B.    f( x ) = e− x+ 3

C.    f( x ) = ex+ 3

D.   f( x ) =−ex  + 4

11.Acandidate’sshareofthevotesvariesdirectlyasthenumberofvotescastforthecandidate. Inacitycouncilelectionwithfourcandidates,Underwoodreceived756votesandearneda28% shareofthevotes.Dixonreceived1,080votes.WhatwasDixon’scorrespondingshareofthe votes?

11.D

12.Thegraphofy=f(x)isshownattheleftandthegraphof y=g(x)isshownattheright.(No formulasaregiven.)Whatistherelationshipbetweeng(x)andf(x)?

12.B

4        y= f(x)                                                         4

2                                                               2

-4      -2               2      4

-2

-4

-4      -2               2      4

-2

-4

y=f(x)                                                           y=g(x)

A.     g(x)=f(x–2)+2

B.     g(x)=f(x–1)–2

C.     g(x)=f(x+1)–2

D.     g(x)=f(x+2)–1

SHORTANSWER:

13.Multiplyandsimplify:(5+8i)(3+i).

Write the answer in the forma + bi, where aand b are real numbers.                                Answer: 7+29i

14.Solve,andwritetheanswerinintervalnotation:

x + 9 ≤ 0 .                       Answer:

x− 4

                                                                                                                                                                                         -9≤x<4

15.Abowlofsoupat165°F.isplacedinaroomofconstanttemperatureof75°F.The

temperatureTofthesoupt minutesafterit isplacedintheroomisgivenby

T(t)=75+90e –0.075 t

Findthetemperatureofthesoup12minutesafterit isplacedintheroom.(Roundto the nearest degree.)

Answer: 112⁰F

  1   

16. Find the value of thelogarithm:  log5  125  .                                                          Answer:  -3

17.Solve:

65x − 7 = 36 .                                                                                Answer:  x=1.8

18.Suppose$6,000isinvestedinanaccountatanannualinterestrateof4.5%compounded continuously.Howlong(tothenearesttenthof ayear)willit taketheinvestmenttodoublein size?                          Answer:  15.4

19. Letf(x)=x2−14x+52.

(a)Find thevertex.                                                                                         Answer: (7, 3)

(b) Statetherangeof thefunction.                                                                       Answer:  3≤y≤∞

(c) On what interval is thefunction increasing?                                                       Answer: 7≤x≤∞

20.ConsiderthepolynomialP(x),shownin both standardformand factored form.

P( x)=−1

x4−1x3+7

x2+41x+ 3=−1( x− 3)( x+ 1)( x+ 2)( x+ 5)

10        2        10        10               10

(a)Which sketch illustratestheend behaviorofthepolynomial function?

                                                                                                            Answer: D

GRAPHC                                                             GRAPHD

21. Let

f( x)=3x− 9.

x− 2

(a)State thedomain.                                                                  Answer: (-∞≤x≤ ∞) except x=2

(b)Statetheverticalasymptote(s).                                            Answer: x=2

(c)Statethehorizontal asymptote.                                            Answer: y=3

(d)Which of the followingrepresentsthe graph of

f(x)=

3x− 9

x− 2

?         Answer: B

GRAPH A.                                                               GRAPHB.

GRAPHC.                                                               GRAPHD.

SHORTANSWER,withworkrequiredtobeshown,asindicated.

( −2a7b2)4 a3b−8

22.Simplify:

a−5

.Showwork.

23.Points(–3,2)and(1,8)are endpointsofthediameterof acircle.

(a)Whatisthelengthof thediameter?Givetheexactanswer,simplifiedasmuchaspossible.

Showwork.

(b)Whatisthecenterof thecircle?

(c)Whatistheequationofthecircle?

24.Findtheequationforalinewhichpassesthroughthepoints(3,–8) and (5,–2).Writethe equationinslope-interceptform.Showwork.

25.Marcia,aresidentof Metropolis,paysMetropolisanannualtax of$46plus2.4%ofher annualincome.If Marciapaid$1,558intax,whatwasMarcia’sincome?Showwork.

Total tax = 46+

26. Letf(x)=4x2+9andg(x)=x+3.

(a) Findthecompositefunction(f  og)(x)andsimplify.Showwork.

(b)Find(f  og) (−5).Showwork.

27.Findtheexactsolutionsandsimplifyasmuchaspossible:2x2+13=2x.Showwork.

28.Giventhefunction

f( x)=1x+ 4,findaformulafortheinversefunction.Showwork.

9

29.DonutDelights,Inc.hasdeterminedthatwhenxdonutsaremadedaily,theprofitPis given by

P(x)=–0.002x2+4.7x–150

(a)Whatisthecompany’sprofitif800donutsaremadedaily?

(b)Howmanydonutsshouldbemadedailyinordertomaximizethecompany’sprofit?Show work.

x−10          42