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

Find the equation that the given graph represents.

1)

1)

-10

A)P(x)=-*3* 4×2+x-5

C) P(x):15 * 4*3 – x2 + 3x –

5

B)P(x)=x3+x2+x+5

D)P(x):x3+ 4;p- x-5

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

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary.

2) t(x) = x3

–

7×2 +15x

–

25

Determine whether the statement is true or false.

3) If f(x) is a polynomial and f(-5) = O then x + 5 is

Z) _

a factor of f(x).

3)

Sketch the graph of the polynomial function.

a)f(x):(x+2)3-l

4)

Find the correct end behavior diagram for the given polynomial function.

5)P(x)=-x5-3×3-8x+1

s)

Use the graph to answer the question.

6) Find the domain and range of the rational function graphed below.

-10

-8 -6 -4

-2

I

6)

.1 68

t-

———-t-‘

——..- i I

r in

t, r’

liro

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

Determine which of the rational functions given below has the following feature(s).

7) The x-intercept is (5, 0)

A)f(x)=#

sir(*r

=i*

c)f(x)=#

7)

D)f(x):**

8) The y-intercept is (0, 4)

6tt*l:#

8)

B)f(x):#

c)f(x):i3

D)f(x):#

9) There is a “hole” in its graph at x = 5

e)

f(x):i*

A)f(x)=#

B)

c)r(x)=#I

(x

+

dr rr*r _ – 5Xx 9)

(x+5)(x-5)

10) The x-axis is its horizontal asymptote

A)f(x)

v

=-

LL) x-intercepts: (-3, 0) and (3, 0),

asymptote: y =

6(,):*

B)f(x):#

-)

10)

D)f(x)

=#

y-intercept[O 9) vertical asymptotes: x : -]” and x = 1, horizontal

1

(x + 3Xx – 3)

A) f(x) _

(x+1)(x-1)

(x

+

O f(x) _ – 3)(x 3)

(x-1)(x+1)

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

Answer the question

12) How can the graph of f(x)

=*

be obtained from the graph of y

2

=

1

7

12)

11)

Give the domain and range for the rational function. Use interval notation.

L

13) f(x)

–

(

1

13)

(x + 4)2

Give the equations of any vertical asymptotes.

r1)

f(x)=#

74)

1s)f(x):*

1s)

Give the equations of any horizontal asymptotes.

16)g(x)=#

17)h(x)

=9xz

‘l*’

18)s(x)

=#

1b)

17)

-8

18)

Give the equation of any oblique asymptotes.

19) h(x)

-6

– 5x+2

= 3xzlx

7e)

20)f(x)=#

20)

Identify any vertical, horizontal, or oblique asymptotes in the gfaph of y= f(x). State the domain of f.

27)

21)

-10 -8 -6 -4

-2

J

Sketch the graph of the rational function.

22)

f(x)=:+

22)

Solve the problem.

23) If the average cost per unit C(x) to produce x units of plywood is given

what is the unit cost for

ty C(x)=ffi,

23)

20 units?

Determine whether or not the function is one-to-one.

24)

24)

2s)

4

Decide whether the given functions are inverses.

26) f = lF3, -6), (0,4), (4, -3), (8, 10)l

g= le6, -3), (4,0),(-3,4), (10, 8))

26)

Use the definition of inverses to detennine whether f and g are inverses.

27)t(x)=2x-4,

28) f(x)

=7x

-7,

g$)=+

g(*)

=|*

27)

*1

28)

If the function is one-to-one, find its inverse. If not, write “not oneto-one.”

29) l(L9,5), (1O -L), (-19,7)l

2e)

30) l(-7, -7), (-6, -7), (-5, -3), (-4, -9l

30)

31) f(x) =6×3 + 4

31)

32) f(x)

32)

=2x+3

Find the function value. If the result is irrational, round your.rnswer to the nearest thousandth.

33) Let

f(x):4x.

34) Let

(.):f+l..Find

Find f(3).

33)

(3).

34)

L’J

Evaluate the logarithm.

3s) log,

1

fr

35)

Write an equivalent expression in exponential form.

36)

log’

625

=4

36)

Write in logarithmic form.

3n

2-2

:!

J/)

Solve the equation.

38)tos7$=x

38)

Use the properties of logarithms to rewrite the expression. Simplify the result

if possible. Assume all variables represent

positive real numbers.

39) 1o9614x6y)

3e)

5

Write the expression as a single logarithm with coefficient

1. Assume

all variables represent positive real numbers with

a+1and b*L.

40) (logn x

– logs y) + 5 logx z

40)

Solve the system by substitution.

41)x+Y=-2

41)

x-Y=-8

Solve the system by elimination.

42) x- 3y:-8

6x – 4Y =)/

42)

Solve the system by substitution.

43) x+7y=27

13)

6x+7Y=$/

If the system has infinitely many solutions, write the solution set with x arbitrary.

44)5x-8y=1

Solve the system.

-10x +

1’6Y

Write the augmented matrix for the system. Do not solve the system.

45) 7x+ 4y= J)

5x+ 3Y:

46)

6x

))

+22= 1.0

4y+72= 26

9x + 3y

44)

=1

+72:

4s)

46)

32

Use the Gauss-Jordan method to solve the system of equations.

If the system has infinitely many solutions, give the

solution with y arbitrary.

47)x+y=J

47)

*-Y=-4

Use the Gauss-|ordan method to solve the system of equations.

variable be the arbitrary variable.

48)

7x-9y- z=-24

x-3y-52=-54

-2x+ y+ z= 7

If

the system has infinitely many solutions, let the last

48)

Find the value of the deterninant

_r)

4e)

l:;l

ls+t

50)lasz

s0)

lr+s

6

1314 REVIEW TEST4 FpJ-LZOI7

1)D

2) 5,7 + 2i,7

3) True

–

2i

4)

v……….

..”…..5

r’l

. l.*

…t,

‘-

-‘5′

.

5)

*o

6j Domain:

(–,

-2) u (-2,

*

Range:

(–, -3) u (-3’ -)

7)B

8)A

e)D

10)

11)

c

A

By making a horizontal shift of 6 units to the right

13) Domain: (–, -4) v (-4, * Range: (0, -)

12-)

14) x

2

=-f,

15)x=3,x=-3

16) none

17)y=3

18)y=0

19) none

20)y=1ag

21) Vertical: x

=2;horizontal: y = -4;

(‘*,2)

u

(2’

*)

22)

.-lA

-.8. -.6.

23) $18.00

24) No

7

Answer Key

Testname: MATH 1314 REVIEW TEST4 FALLZOIT

25) Yes

26) Yes

27) No

28) Yes

29) l(5 , 79) , (-7 , 70),

(7

, -79)l

30) not one-to-one

31) f-1(x) =

32) f-1(x)

zffi

^ll6

=+

33) 64

zqt1:rx

3s) -2

36) 54 = 625

37)

togrj.=-z

38) {-2}

39) logu4 + 6logax + logaY

4o)rog2ttrl

41) {(-5,3)}

42)

V,s)l

43) t(6,3))

44) a

4s)

46)

tliE l

l”:-l;21

lo z zlzz l

44{- +,+

48)

{(3,4,9)l

4e) 62

s0) 6

8

…

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