College Algebra 30 questions

CollegeAlgebraQuiz6.pdf

Home >Mathematics homework help >Algebra homework help >College Algebra 30 questions

College Algebra MATH 107

Record your answers and work on the separate Answer sheet provided.

There are 30 problems. Problems #1-12 are Multiple Choice. Problems #1311are Short Answer. (Work not required to be shown) Problems #2210 are Short Answer with work required to be shown.

MTILTIPLE CHOICE

1. Determine the domain and range of the piecewise function.

Domain [-1,0]; Range [2, 3] Domain [-1,3]; Range [0,4] Domain lll2,4l; Range [0, 3] Domain [0,4]; Range [-1, 3]

2. Solve: J3r-5 = x-3

1',7

7 No solution

A. B. C. D.

Summer, 2018, V3.3

)

A. B. C. D.

This is an open-book exam. You may refer to your text and other course materials as on the exam, and you may use a calculator.

Page 1 of1I

College Algebra MATI{ 107

3. Determine the interval(s) on which the function is inoeasing.

Summer, 2018, V3.3

(-o, -0.5) and (5, 6.5)

(- 0.5, 3)

(1, 5)

(-2,2)

4. Determine whether the gaph of y = x2 +3 is symmetric with respect to the origrn, the x-axis, or they-axis. 4.

A. symmetic with respeot to the y-a:ris only B. symmetric with respect to the x-anis only C. slmmotric with respect to the origtn only D. no1 symmetric with respectto thex-ari$ not sSmmetric with rcspect to they-CIris, and

not symmetric with respect to the odgin

5. Solvq and express the answer in int€rval notation: | 6 - 5x | < 4.

A. (-a,215) B. [215,21 C. (-o,21u [2/5, co) D. (-c,2/51u [2, o)

Page2ofll

CeltqpAtee€- [4AT[Iry/

6" Slhietu ofthe followins rrycwa fu paptu sf k * 1y * 14 ?

@,*BI&Y.3.S

hgp 3 d11

20. Consids the polyrourial P(r), shorrn in both safldard ftrm and &atored fonn.

P(d = * r* * * r' ** *' - * * - z= { 1x + 5}(r + 4)(x + 1)(s - 1)10 l0 10 t0 l0' (a) Whi*.h skr*eh iuq*r-dcs ths end berhavior oftb polynomid fimetiou?

A.A

{

B.A \\

v "'t**f D. ,fl\

Cetep Algebtrs il,rAIII l&7

(b) $tde the mo* sf&s firc{im.

(e) Shtethey.iutscept

(d) Sete ueich Sr@ belw is tu g@ of P(x).

GRAPTIA GRAPHB

GRAPH D

Srrma,2018, V3.3

Answm:

Answer:

Answm:

Annurer:

GRAPHC

PaGp I ofll

t: Colle*pAISSra ],IATII 107

')t-1, /

zl.l,et. f(x)= :x-5 (a) Stutethe dmain

(b) State thohoriuotrtal aqrmptotE

(d) Shich of the follouring mpsesar$s th gr-aph of f (i,=# ?

GR^APHA. GRAPHB,

GRAPH C.

$ulw,2O1&V3.3

Answer:

Arswpr;

Angftr€f:

GRAPH D.

Pagr I ofll

College Algebra MATH 107 Summer, 2018, V3.3

SHORT ANSWER, with work required to be shown, as indicated.

22.Let f (x)= x - 72 and g(x) = J;:T . /t\

(a) Find I /- lfql. Show work. \ g,r

(b) Find the domain ofthe quotient function /. E*plain. oo

23. Points (-5, 9) and (-7, 1) are endpoints of the diameter of a circle.

(a) What is the length of the diameter? Give the exact answer, simplified as much as possible. Show work (b) What is the center point C of the circle? (c) Given the point C you found in part (b), state the point symmetric to C about the r-uris.

Z4,Findthe equation for a line which passes through the points (6,-2) and (4, 8). Write the equation in slope-intercept form. Show work

25. Sara, a resident of Metropolis, pays Metropolis an annual tax of $85 plus 1 .2o/o of her annual income. If Sara paid $991 in tax, what was Sara's income? Show work

26.Letf (x)=Zf + 9 and g(x) =r-4.

(a) Find the composite function U od@)and simplifu. Show worlc (b) Find (/og)(-z). Show work.

2T.Findthe exact solutions and simpliff as much as possible: 2* :3 + 8x. Show work

28. Given the function .f (x) =: - I , , find a formula for the inverse function. Show worlc 9

Page l0ofl1

ehgpAlgebfift lt{AII{ 107 &mffi,.2{r^l&V3.3

7. Write a slope.irfiercopt equstion for a line parallol to the line.$ - 5y = I whieh pssses through ?"thopoiu(-10, $.

I A. y=-lx+3

)

B. l^

v = -x+J-5

.y=5s+53C;

D. v=1x+5''5

L Doec the graph below ltpresent a f-unqtioo and in it one"to-one?

It is afimcttoa aad itis qn€@" lt is a fimction:but not one-ts-me. It is not a function but it is one-to-one. It is not a ftnction aid it i nCIt on€-to-one.

A. B. c. D.

Pagp 4 offl

College Algebra MATH 107 Summer, 2018, V3.3

29. The fuel efficiency F for a particular cm is given by

F(x) : *0.015 * + t.32 x + 15.9 where.rr is the speed of the car in miles per hour (mph) and F(.r) is the corresponding fuel efficiency in miles per gallon (mpg).

(a) What is the fuel efficiency if the car's speed is 70 mph?

(b) What speed will yield the maximum fuel efficiency? Show work

30. Solve: x-7 * -20 =0. Showworlcx-5 x'-25

Page ll ofll

Co{egeAtgsbril MATH 10,

9. Express as an equivalent expression:

A. log(8y+a-r)

los(8y)

8 logy +log I - loe (x* 3)

Sumqr20l&V33

Ios(x*4

*[*)

*[*#J

10.

A. f(x)=3e-* B. f{x *2+{x e. .f(x)=2*u' o. /(r)= 2*{

I 0. lUhieh of flre firnctions

Page 5 ofll

CollegeAlgebra MATH 107

11. Suppose that for a firnction/, .f has nox-intercepts.

Which ofthe following statements MU$T be true?

A. f (x)>0 for all x in the domain ofl B. f is an invertible funotion. C. The equation f (0) = y has no real-number solutions. D. The equ*tion"f(x) = 0 has no real-number solutions.

Summer,2018, V3.3

11.

12.Thegaph ofy=f(x) isshownattheleftandthegaphofy=g(x)isshownattheright.(No formulas are give,n.) What is the relationship betwen g(.r) and/(x)?

12.

y:.f(x\ v=8{g)

g(r) */(x- 1) s(x) =1(x) + I s(x) =/(x + 1) g(x) *f(x+2)

A. B. C. D.

Paes 6 ofll

College Algebra MATH 107 Summer, 2018, V3.3

SHORT ANSWER: 13. Multiply and simpliff: (6 - r)(7 + 3r).

Writethe answer inthe form a * bi,where a and barereal numbers. Answer:

14. Solve, and write the answer in intsrval notation: '*1 =

o.x-l Answer:

15.Abowlof soup et175" F.isplacedinaroomofconstanttemperatureofT0oF. The temperature Z of the soup / minutes after it is placed in the room is given by

T(t):70 + 105 e-o'o,s t

Find the temperature of the soup 18 minutes after it is placed in the room. (Round to the nearest degree')

Answer:

16. Find the value ofthe logarithm: Answer: ""

(*)

17. solve: 33x+9 =64. Answer:

18. Suppose $5,700 is invested in an account at an annual interest rute of 2.5Yo compounded continuously. How long (to the nearest tenth of a year) will it take the investment to double in size? Answer:

rg.Letf (x): * + lbc + 37 . (a) Find the vertex.

(b) State the range of the function.

Answer:

Page 7 ofll