Chapter 2: Polynomial and Rational Functions...Larson’s Precalculus with Limits: A Graphing...

69 © 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed

with a certain product or service or otherwise on a password-protected website for classroom use.

Name: __________________________ Date: _____________ Chapter 2: Polynomial and Rational Functions

1. Use long division to divide. ( ) ( )4 2 2 – – 5 + 4 – 1x x x x÷

A) 2 – 4 + 4x x B) 2 + 4 – 4x x

C) 22

–68 + 11 – 4 + 16 + 4 – 1

xx xx x

+

D) 22

–5 1 + 4 – 4 + 4 – 1

xx xx x

−+

E) 22

4 – 4 + 4 – 4 + 4

x xx x

−

2. Write 4 3 2( ) – 12 + 59 – 138 + 130f x x x x x= as a product of linear factors. A) ( )( )( )( )3 3 2 3 2 2x i x i x i x i− − − + − − − +

B) ( )( )( )( )3 3 2 2x i x i x i x i− − − + − − − +

C) ( )( )( )( )3 3 + 3 2 2x i x i x i x i− − − + − − +

D) ( )( )( )( )3 3 – 2 3 – 2 3x i x i x i x i− + − − + −

E) ( )( )( )( )3 3 – 3 2 – 3 2x i x i x i x i− + − − + −

3. Find the zeros of the function below algebraically, if any exist. 5 3( ) – 5 + 4f x x x x= A) –4, –1, 1, 4 B) –4, –2, 2, 4 C) –2, –1, 0, 1, 2 D) –4, –2, 0, 2, 4 E) No zeros exist.

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.

Precalculus with Limits A Graphing Approach Texas Edition 6th Edition Larson Test BankFull Download: http://testbanklive.com/download/precalculus-with-limits-a-graphing-approach-texas-edition-6th-edition-larson-test-bank/

Full download all chapters instantly please go to Solutions Manual, Test Bank site: testbanklive.com

http://testbanklive.com/download/precalculus-with-limits-a-graphing-approach-texas-edition-6th-edition-larson-test-bank/

Larson’s Precalculus with Limits: A Graphing Approach, Texas Edition



4. Find two positive real numbers whose product is a maximum and whose sum of the first number and four times the second is 200 . A) 160, 10 B) 116, 21 C) 108, 23 D) 100, 25 E) 76, 31

5. Determine the equations of any horizontal and vertical asymptotes of 2

2( )+ 16xf x

x= .

A) horizontal: 4y = ; vertical: –4x = B) horizontal: 1x = ; vertical: none C) horizontal: –4y = ; vertical: 1x = D) horizontal: 1y = ; vertical: none E) horizontal: none; vertical: none

6. Find a polynomial function with following characteristics.

Degree: 4

Zero: –1, multiplicity: 2 Zero: –3 , multiplicity: 2

Falls to the left, Falls to the right

Absolute value of the leading coefficient is one A) 4 3 2 – 4 + 22 + 24 + 3y x x x x= B) 4 3 2 – 4 + 12 + 9y x x x= − C) 4 3 2 – 6 – 18 + 10 + 3y x x x x= D) 4 3 2 – 8 – 22 – 24 – 9y x x x x= − E) 4 3 – 8 – 24 + 9y x x x= −

7. A polynomial function f has degree 3, the zeros below, and a solution point of ( )–3 –4.f = Write f in completely factored form.

–4, –3 + 2i A) ( ) ( )( )( )+ 3 + 4 – 2 + 4 + 2f x x x i x i=

B) ( ) ( )( )( )– + 4 + 2 – 3 + 2 + 3f x x x i x i=

C) ( ) ( )( )( )+ 4 + 2 – 3 + 2 + 3f x x x i x i=

D) ( ) ( )( )( )– + 4 + 3 – 2 + 3 + 2f x x x i x i=

E) ( ) ( )( )( )+ 4 + 3 – 2 + 3 + 2f x x x i x i=

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.

Chapter 2: Polynomial and Rational Functions



8. The interest rates that banks charge to borrow money fluctuate with the economy. The interest rate charged by a bank in a certain country is given in the table below. Let t represent the year, with t = 0 corresponding to 1986. Use the regression feature of a graphing utility to find a quadratic model of the form 2y at bt c= + + for the data.

Year t

Percent y

1986 12.4 1988 9.7 1990 7.3 1992 6.3 1994 9.7 1996 11.6

A) 2–2.13 +12.61 + 0.21y t t= B) 212.61 + 0.21 – 2.13y t t= C) 20.21 – 2.13 +12.61y t t= D) 20.17 – 2.58 +10.59y t t= E) 20.25 –1.73 +14.37y t t=

9. Find the zeros of the function below algebraically, if any exist. 3 2( ) 25 – 60 + 36f x x x x=

A) 65

− and 0

B) 0 and 65

C) 6 ,5

− 0, and 65

D) 65

− and 65

E) No zeros exist.

10. Determine the zeros (if any) of the rational function 2 – 64( )

+ 5xf xx

= .

A) x = –5

B) 8 8– ,5 5

x x= =

C) x = –64, x = 64 D) x = –8, x = 8 E) no zeros

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




11. The graph of the function

is shown below. Determine the domain.

A) B) C) D) E)

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




12. Which of the given graphs is the graph of the polynomial function below?

( ) 5 33 1– –2 2

h x x x x=

Graph 1 :

Graph 2 :

Graph 3 :

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




Graph 4 :

Graph 5 :

A) Graph 2 B) Graph 5 C) Graph 4 D) Graph 1 E) Graph 3

13. Perform the addition or subtraction and write the result in standard form. ( ) ( )7.2 –12.3 8.1 –1.21i− − −

A) –15.3+13.4 i B) 0.9 +13.4 i C) –0.9 +11.2 i D) –15.3+11.2 i E) 15.3+13.4 i

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




14. Find a fifth degree polynomial function of the lowest degree that has the zeros below and whose leading coefficient is one.

–3, –1, 0, 1, 3 A) ( ) 5 4 3 2+ 7 –19 – 32 + 48f x x x x x x=

B) ( ) 5 4 3 2+ 7 –19 + 32 + 48f x x x x x x=

C) ( ) 5 4 3 2+ 4 –13 + 3 +12f x x x x x x=

D) ( ) 5 4 3 2+ 5 –13 + 27 + 36f x x x x x x=

E) ( ) 5 3–10 + 9f x x x x=

15. Find the zeros of the function below algebraically, if any exist.

( ) 6 3– 9 +8f x x x= A) 1 and 2 B) –4 and 1 C) –4 and 2 D) –4, –1, 1, and 4 E) –4, –2, 2, and 4

16. Identify any horizontal and vertical asymptotes of the function below.

( ) 2 – 8+ 6

xf xx

=

A) vertical asymptotes: –2x = and 2;x = horizontal asymptotes: –6y = and 6y = B) vertical asymptotes: –2x = and 2;x = horizontal asymptotes: none C) vertical asymptotes: –6x = and 6;x = horizontal asymptotes: none D) vertical asymptotes: none; horizontal asymptotes: –2y = and 2y = E) vertical asymptotes: –6x = and 6;x = horizontal asymptotes: –2y = and 2y =

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




17. Find all the rational zeros of the function 5 4 3 2( ) –2 – 11 – 19 – 17 – 17 – 6f x x x x x x= .

A) 1 , –3, –12

x =

B) 2– ,1, –23

x =

C) 1 3– , , –22 2

x =

D) 1 3– ,2 2

x =

E) 1– , –3, –22

x =

18. Find real numbers a and b such that the equation –10 + 10a bi i+ = is true. A) 10, –10a b= = B) –10, –10a b= = C) 10, 10a b= = D) –10, 10a b= = E) –20, 0a b= =

19. Use long division to divide. ( ) ( )3 2 + 3 + + 3 + 3x x x x÷

A) 2 + 3x

B) 2 53 + 6 + 17 + 3

x xx

−

C) 2 48 + 6 + 19 + 3

x xx

+

D) 2 + 6 + 17x x E) 2 + 1x

20. Find two positive real numbers whose product is a maximum and whose sum is 146 . A) 71, 75 B) 73, 73 C) 78, 68 D) 82, 64 E) 61, 85

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




Answer Key

1. C 2. E 3. C 4. D 5. D 6. D 7. D 8. C 9. B

10. D 11. A 12. C 13. A 14. E 15. A 16. D 17. E 18. D 19. E 20. B

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




Name: __________________________ Date: _____________

1. Describe the right-hand and the left-hand behavior of the graph of

( )3 24( ) – + 5 + 8 17

t x x x x= + .

A) Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right.

B) Because the degree is odd and the leading coefficient is negative, the graph rises to the left and falls to the right.

C) Because the degree is odd and the leading coefficient is negative, the graph falls to the left and rises to the right.

D) Because the degree is odd and the leading coefficient is positive, the graph rises to the left and rises to the right.

E) Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right.

2. If 25

x = is a root of 3 225 – 70 + 44 – 8 0x x x = , use synthetic division to factor the

polynomial completely and list all real solutions of the equation.

A) ( )( )( )5 – 2 5 + 2 – 2x x x ; 2 2, – , 25 5

x =

B) ( ) ( )25 + 2 – 2x x ; 2– , 25

x =

C) ( )( )25 – 2 – 2x x ; 2 , 25

x =

D) ( )( )25 + 2 – 2x x ; 2– , 25

x =

E) ( ) ( )25 – 2 – 2x x ; 2 , 25

x =

3. Simplify ( ) ( )2 23 – 6 3 + 6i i− and write the answer in standard form. A) 0 B) –72 i C) 18 – 72 i D) 18 + 72 i E) 6 – 24 i

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




4. Determine the domain of 2

6 + 6( )– 6

xf xx x

= .

A) all real numbers except 1, 0, and 6x x x= − = = B) all real numbers except 0 and 6x x= = C) all real numbers except –6 and 1x x= = − D) all real numbers except 6x = E) all real numbers

5. Suppose the IQ scores (y, rounded to the nearest 10) for a group of people are summarized in the table below. Use the regression feature of a graphing utility to find a quadratic function of the form 2y ax bx c= + + for the data.

IQ Score y

Number of People x

70 50 80 76 90 89 100 93 110 74 120 53 130 16

A) 2–0.04 +15.08 – 411.58y x x= B) 2–0.06 +12.06 – 484.21y x x= C) 2–0.08 +10.98 – 508.43y x x= D) 2–0.07 +13.63 – 460y x x= E) 2–0.09 +8.56 – 556.85y x x=

6. Simplify f below and find any vertical asymptotes of f.

( )2 – 25

+ 5xf xx

=

A) ( ) + 5,f x x= 5;x ≠ vertical asymptotes: none

B) ( ) – 5,f x x= –5;x ≠ vertical asymptotes: none

C) ( ) – 5,f x x= 5;x ≠ vertical asymptotes: none

D) ( ) + 5,f x x= –5;x ≠ vertical asymptotes: –5x =

E) ( ) – 5,f x x= 5;x ≠ vertical asymptotes: 5x =

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




7. Find the quadratic function f whose graph intersects the x-axis at ( )2,0 and ( )3,0 and

the y-axis at ( )0, –18 .

A) ( ) 23 + 3 + 9f x x x=

B) ( ) 2–3 +15 –18f x x x=

C) ( ) 2–3 – 3 + 6f x x x=

D) ( ) 23 – 3 –18f x x x=

E) ( ) 23 –15 –18f x x x=

8. Using the factors ( )–5 + 2x and ( )– 1x , find the remaining factor(s) of 4 3 2( ) 10 + 31 – 84 + 53 – 10f x x x x x= and write the polynomial in fully factored form.

A) ( )( )( )( )( ) –5 + 2 –5 + 2 2 – 1 – 1f x x x x x=

B) ( )( )( )( )( ) –5 + 2 – – 5 2 – 1 – 1f x x x x x=

C) ( ) ( )( )2( ) –5 + 2 2 – 1 + 1f x x x x=

D) ( )( ) ( )2( ) –5 + 2 – + 5 + 1f x x x x=

E) ( ) ( )2 2( ) –5 + 2 – 1f x x x=

9. Simplify 4 + 35 + 2

ii

and write the answer in standard form.

A) 26 7– +29 29

i

B) 26 7–29 29

i

C) 26 7+29 29

i

D) 7 26+29 29

i

E) 7 26–29 29

i

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




10. Write the complex conjugate of the complex number –5 10 i− . A) 5 10 i− B) –5 –10 i− C) 5 –10 i− D) –5 10 i+ E) 5 10 i+

11. Determine the value that 2

4 6( )7

xf xx

−=−

approaches as x increases and decreases in

magnitude without bound. A) 8 B) 6 C) 4 D) 2 E) 0

12. Find all real zeros of the polynomial 4 3 2( ) + 13 + 40f x x x x= and determine the mutiplicity of each. A) 0x = , multiplicity 2; –8x = , multiplicity 1; –5x = , multiplicity 1 B) 8x = , multiplicity 2; 5x = , multiplicity 2 C) 0x = , multiplicity 2; 8x = , multiplicity 1; 5x = , multiplicity 1 D) –8x = , multiplicity 2; –5x = , multiplicity 2

E) 0x = , multiplicity 1; 8x = , multiplicity 1; –8x = , multiplicity 1; 5x = , multiplicity 1

13. Given 3 i+ is a root, determine all other roots of 4 3 2( ) – 10 + 42 – 88 + 80f x x x x x= . A) 3 , 2 2 , 2x i i i= + ± − B) 3 , 2x i i= − ± C) 3 , 2 2 , 2x i i i= − − + D) 3 , – 2 2x i i= − ± E) 3 , 2 2x i i= − ±

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




14. Determine the zeros (if any) of the rational function 2 – 9( )– 2

xf xx

= .

A) x = 2

B) 3 3, –2 2

x x= =

C) x = –9, x = 9 D) x = –3, x = 3 E) no zeros

15. Determine the zeros (if any) of the rational function 3

2

– 1( )+ 5

xg xx

= .

A) x = –1, x = 1 B) x = 1 C) 5, 5, 1x x x= − = = D) 5, 5, –1, 1x x x x= − = = = E) no zeros

16. Match the equation with its graph.

A)

B)

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




C)

D)

E)


3( ) 7+ 7

g xx

= + .

A) 7, 7x x= − = B) –3x =

C) 3 3– ,7 7

x x= =

D) x = –7, x = 7 E) no zeros

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




18. Find all zeros of the function ( )( )( )( ) + 6 + 3 – 3f x x x i x i= .

A) 6, – 3 , 3x i i= B) –6, 3x i= C) –6, – 3, 3x = D) –6, – 3 , 3x i i= E) –6x =


4 2( ) 2 +10 +12f x x x= A) 3,− 2,− 2, and 3 B) 3,− 0, and 3 C) 3− and 3 D) 2− and 2 E) No zeros exist.

20. Simplify 2 + 53

ii


A) 5 2– –3 3

i

B) 5 2–3 3

i

C) 5 2+3 3

i

D) 2 5+3 3

i

E) 2 5– +3 3

i

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




Answer Key

1. B 2. E 3. B 4. B 5. B 6. B 7. B 8. B 9. C

10. D 11. E 12. A 13. E 14. D 15. B 16. E 17. E 18. D 19. E 20. B

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




Name: __________________________ Date: _____________


2. Write the complex conjugate of the following complex number and then multiply the number by the complex conjugate. Write the result in standard form. 1 –20+ A) 1– 20 i ; 19 B) 1 5 2 i− ; 21 C) –1 2 5 i− ; 21 D) –1 2 5 i− ; 19 E) 1 2 5 i− ; 21

3. Use synthetic division to divide. ( ) ( )3 22 – 5 – 22 – 15 – 5x x x x÷

A) 22 – 3 – 5x x B) 22 + 5 + 3x x C) 22 – 2 – 15x x D) 22 – 7 + 6x x E) 22 + 5 + 2x x

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




4. Sketch the graph of the rational function below.

( )2 –1xf xx

=

A)

B)

C)

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




D)

E)

5. Use long division to divide. ( ) ( )22 + 11 + 12 + 4x x x÷

A) 882 + 19 + + 4

xx

B) 2 + 3x

C) 222 + 19 + + 4

xx

D) 2 + 22x E) –2 – 3x

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




6. Sketch the graph of the quadratic function below.

( ) 2– – 4 –1h x x x=

A)

B)

C)

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




D)

E)

7. If 4x = is a root of 3 2 + 5 – 16 – 80 0x x x = , use synthetic division to factor the polynomial completely and list all real solutions of the equation. A) ( )( )( ) – 5 – 4 + 4x x x ; 5, 4, – 4x =

B) ( )( )( ) + 5 – 4 + 4x x x ; –5, 4, – 4x =

C) ( )( )2 + 5 – 4x x ; –5, 4x =

D) ( ) ( )2 + 5 – 4x x ; –5, 4x =

E) ( )( )( ) + 5 – 5 + 4x x x ; –5, 5, – 4x =

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




8. Simplify –1 – 57

ii


A) 5 +7 7

i

B) 5– +7 7

i

C) 5– –7 7

i

D) 1 5– –7 7

i

E) 1 5–7 7

i

9. Find all the rational zeros of the function 4 3 2( ) 3 – 16 – 59 + 400 – 400f x x x x x= .

A) 3–4,5, –5, –4

x =

B) 3, –20,5x =

C) 44,5, –5,3

x =

D) 4 5 4– , , , – 55 3 3

x =

E) 5 43, –20, ,3 3

x =

10. Use long division to divide. ( ) ( )3 + 27 + 3x x÷

A) 2 – 3 + 9x x B) 2 9x − C) 2 + 3 – 9x x D) 2 9x +

E) 2 39 + 3

xx

− +

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




11. Find all real zeros of the polynomial 3 2( ) + 3 – 49 – 147f x x x x= and determine the mutiplicity of each. A) 7x = , multiplicity 2; –3x = , multiplicity 1 B) 7x = , multiplicity 1; –7x = , multiplicity 1; –3x = , multiplicity 1 C) –3x = , multiplicity 2; –7x = , multiplicity 1 D) –7x = , multiplicity 1; 3x = , multiplicity 1; –3x = , multiplicity 1 E) –3x = , multiplicity 3

12. Use long division to divide. ( ) ( )3 + 4 – 1 + 2x x x÷

A) 2 17 – 2 + 8 – + 2

x xx

B) 2 15 + 2 + 8 – + 2

x xx

C) 2 3 + 2 – + 2

xx

D) 2 3 – 2 + + 2

xx

E) 2 17 + 2 – 8 + + 2

x xx

13. Find real numbers a and b such that the equation 10 – 12a bi i+ = is true. A) –10, 12a b= = B) 10, 12a b= = C) –10, –12a b= = D) 10, –12a b= = E) 22, –2a b= =

14. Determine the x-intercept(s) of the quadratic function 2( ) – 10 + 26f x x x= . A) ( ) ( )0,0 , 4,0

B) ( ) ( )5,0 , 10,0

C) ( ) ( )7,0 , 2,0

D) ( ) ( )0,0 , 2,0 E) no x-intercept(s)

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




15. Determine the domain of 2

3 + 3( )– 3

xf xx x

= .

A) all real numbers except 1, 0, and 3x x x= − = = B) all real numbers except 0 and 3x x= = C) all real numbers except –3 and 1x x= = − D) all real numbers except 3x = E) all real numbers

16. Perform the following operation and write the result in standard form.

9 29 9

ii i

++ −

A) 9 8340 80

i+

B) 27 8310 10

i+

C) 1 941 82

i+

D) 27 8382 82

i+

E) 27 838 8

i+


Year t

Percent y

1986 12.1 1988 10.1 1990 6.8 1992 6.6 1994 8.6 1996 12.0

A) 2–2.23 +12.61 + 0.22y t t= B) 212.61 + 0.22 – 2.23y t t= C) 20.22 – 2.23 +12.61y t t= D) 20.17 – 2.69 +10.59y t t= E) 20.26 –1.8 +14.37y t t=

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




18. Which of the following is the graph of the given equation?

A)

B)

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




C)

D)

E)

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




19. Simplify ( )11–2 and write the answer in standard form.

A) 32 2 i B) –32 2 i C) 1024 2 i D) –32 2 E) The expression cannot be simplified.

20. Determine whether the scatter plot could best be modeled by a linear model, a quadratic model, or neither.

A) linear model B) quadratic model C) neither

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




Answer Key

1. B 2. E 3. B 4. E 5. B 6. A 7. B 8. B 9. C

10. A 11. B 12. A 13. D 14. E 15. B 16. D 17. C 18. D 19. B 20. B

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




Name: __________________________ Date: _____________

1. Use the regression feature of a graphing utility to find a quadratic model for the data below.

x y −2 9.8 −1 4.1 0 3.3 1 6.6 2 13.8 3 24.1 4 39.5

A) 21.91 +1.06 + 3.15y x x= B) 21.81 +1.02 + 3.3y x x= C) 22.21 + 0.92 + 3.3y x x= D) 22.11 + 0.87 + 3.65y x x= E) 22.01 + 0.97 + 3.44y x x=

2. Find a fifth degree polynomial function of the lowest degree that has the zeros below and whose leading coefficient is one.

–4, –1, 0, 1, 4 A) ( ) 5 4 3 2+ 4 –13 + 27 + 36f x x x x x x=

B) ( ) 5 4 3 2+ 4 –13 – 27 + 36f x x x x x x=

C) ( ) 5 4 3 2+ 5 –19 –16 + 48f x x x x x x=

D) ( ) 5 4 3 2+ 7 –13 – +12f x x x x x x=

E) ( ) 5 3–17 +16f x x x x=

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.





Year t

Percent y

1986 12.8 1988 10.0 1990 6.9 1992 5.7 1994 8.6 1996 12.7

A) 2–2.7 +13.35 + 0.26y t t= B) 213.35 + 0.26 – 2.7y t t= C) 20.26 – 2.7 +13.35y t t= D) 20.21 – 3.26 +11.22y t t= E) 20.32 – 2.18 +15.22y t t=

4. Find all real zeros of the polynomial 4 3 2( ) + 8 + 12f x x x x= and determine the mutiplicity of each. A) 0x = , multiplicity 2; –2x = , multiplicity 1; –6x = , multiplicity 1 B) 2x = , multiplicity 2; 6x = , multiplicity 2 C) 0x = , multiplicity 2; 2x = , multiplicity 1; 6x = , multiplicity 1 D) –2x = , multiplicity 2; –6x = , multiplicity 2

E) 0x = , multiplicity 1; 2x = , multiplicity 1; –2x = , multiplicity 1; 6x = , multiplicity 1

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




5. Which of the given graphs is the graph of the polynomial function below?

( ) 5 33 1+ –2 2

h x x x x=

Graph 1 :

Graph 2 :

Graph 3 :

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




Graph 4 :

Graph 5 :

A) Graph 1 B) Graph 4 C) Graph 3 D) Graph 5 E) Graph 2


B) ( ) ( )6,0 , 15,0

C) ( ) ( )8,0 , 3,0


Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




7. Find a polynomial function with following characteristics.

Degree: 4 Zero: 4 , multiplicity: 2 Zero: –3 , multiplicity: 2

Falls to the left, Falls to the right

Absolute value of the leading coefficient is one A) 4 3 2 + – 23 + 24 – 12y x x x x= B) 4 3 2 + – 48 + 9y x x x= − C) 4 3 2 – 6 – 18 + 25 + 48y x x x x= D) 4 3 2 + 2 + 23 – 24 – 144y x x x x= − E) 4 3 + 2 – 24 – 36y x x x= −

8. Use synthetic division to divide. ( ) ( )3 – 75 + 250 – 5x x x÷

A) 2 + 5 – 50x x B) 2 – 5 – 75x x C) 2 + 10 + 25x x D) 2 + 15 + 50x x E) 2 + 25 – 10x x


4 2( ) +8 +15f x x x= A) 5,− 3,− 3, and 5 B) 3,− 0, and 3 C) 3− and 3 D) 5− and 5 E) No zeros exist.

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




10. A polynomial function f has degree 3, the zeros below, and a solution point of ( )1 –96.f = Write f in completely factored form.

–2, –3 + 4i

A) ( ) ( )( )( )+ 3 + 2 – 4 + 2 + 4f x x x i x i=

B) ( ) ( )( )( )– + 2 – 4 – 3 – 4 + 3f x x x i x i=

C) ( ) ( )( )( )+ 2 – 4 – 3 – 4 + 3f x x x i x i=

D) ( ) ( )( )( )– + 2 + 3 – 4 + 3 + 4f x x x i x i=

E) ( ) ( )( )( )+ 2 + 3 – 4 + 3 + 4f x x x i x i=

11. Describe the right-hand and the left-hand behavior of the graph of 5 3( ) 7 + + 7q x x x= .

A) Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right.

B) Because the degree is odd and the leading coefficient is positive, the graph rises to the left and falls to the right.

C) Because the degree is odd and the leading coefficient is positive, the graph falls to the left and rises to the right.

D) Because the degree is odd and the leading coefficient is positive, the graph rises to the left and rises to the right.

E) Because the degree is even and the leading coefficient is positive, the graph rises to the left and rises to the right.


( ) 5 3 2– 9 + 27 – 243f x x x x= A) –2 and 2 B) –4 and 2 C) –4 and 4 D) –3 and 4 E) –3 and 3

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




13. Determine the vertex of the graph of the quadratic function 2 5( ) – +4

f x x x= .

A) 1 3,2 2

⎛ ⎞⎜ ⎟⎝ ⎠

B) 5–1,4

⎛ ⎞⎜ ⎟⎝ ⎠

C) 1 5– ,2 4

⎛ ⎞⎜ ⎟⎝ ⎠

D) 1 3– , –4 4

⎛ ⎞⎜ ⎟⎝ ⎠

E) 1 ,12

⎛ ⎞⎜ ⎟⎝ ⎠

14. Write the standard form of the equation of the parabola that has a vertex at ( )3,8 and

passes through the point ( )5, –2 .

A) ( )21( ) – – 3 + 52

f x x=

B) ( )25( ) – – 3 + 82

f x x=

C) ( )210( ) – + 3 + 89

f x x=

D) ( )28( ) – 8 – 25

f x x=

E) ( )28( ) – 8 – 59

f x x=


Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.





2( ) 7+ 7

g xx

= + .

A) 7, 7x x= − = B) –2x =

C) 2 2– ,7 7

x x= =

D) x = –7, x = 7 E) no zeros

17. Determine the domain of the function 2

2

+ 7 + 12( )+ 16

x xf xx

= .

A) Domain: all real numbers except –4 and 3x = B) Domain: all real numbers except –16x = C) Domain: all real numbers except –4 and – 3x = D) Domain: all real numbers except 4 and 3x = E) Domain: all real numbers

18. Write the complex conjugate of the complex number 3 2 i− . A) –3 2 i− B) 3 –2 i− C) –3 –2 i− D) 3 2 i+ E) –3 2 i+

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




19. Match the equation with its graph.

A)

B)

C)

D)

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




E)

20. Write 3 2( ) – 11 + 18 + 25f x x x x= in the form ( ) ( )( )f x x k q x r= − + when 6 6k = + .

A) ( ) ( ) ( )2( ) 6 6 –5 6 6 6 – 5f x x x x⎡ ⎤ ⎡ ⎤= + + + + − −⎣ ⎦ ⎣ ⎦

B) ( ) ( ) ( )2( ) 6 6 –5 6 6 6 + 5f x x x x⎡ ⎤ ⎡ ⎤= + + + + − −⎣ ⎦ ⎣ ⎦

C) ( ) ( ) ( )2( ) 6 6 –5 6 6 6 + 5f x x x x⎡ ⎤ ⎡ ⎤= − + + + − −⎣ ⎦ ⎣ ⎦

D) ( ) ( ) ( )2( ) 6 6 –5 6 6 6 – 5f x x x x⎡ ⎤ ⎡ ⎤= − + + + − −⎣ ⎦ ⎣ ⎦

E) ( ) ( ) ( )2( ) 6 6 –5 6 6 6 – 5f x x x x⎡ ⎤ ⎡ ⎤= + + − + − −⎣ ⎦ ⎣ ⎦

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




Answer Key

1. E 2. E 3. C 4. A 5. C 6. E 7. D 8. A 9. E

10. D 11. C 12. E 13. E 14. B 15. B 16. E 17. E 18. D 19. E 20. D

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




Name: __________________________ Date: _____________

1. Find all the rational zeros of the function 4 3 2( ) 2 – 9 – 41 + 225 – 225f x x x x x= .

A) 2–3,5, –5, –3

x =

B) 2, –15,5x =

C) 33,5, –5,2

x =

D) 3 5 3– , , , – 55 2 2

x =

E) 5 32, –15, ,2 2

x =

2. Using the factors ( ) + 4x and ( )+ 3x , find the remaining factor(s) of 3 2( ) + 6 + 5 – 12f x x x x= and write the polynomial in fully factored form.

A) ( )( )( )( ) + 4 + 3 – 1f x x x x=

B) ( )( )2( ) + 4 + 3f x x x=

C) ( )( )( )( ) + 4 + 3 + 1f x x x x=

D) ( ) ( )2( ) + 4 + 3f x x x=

E) ( )( )( )( ) + 4 + 3 + 3f x x x x=

3. Find the quadratic function f whose graph intersects the x-axis at ( )1,0 and ( )4,0 and

the y-axis at ( )0, 4 .

A) ( ) 2– – 3 – 4f x x x=

B) ( ) 2 – 5 + 4f x x x=

C) ( ) 2 + 3 + 4f x x x=

D) ( ) 2– + 3 + 4f x x x=

E) ( ) 2– + 5 + 4f x x x=

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.





( )2 +1xf xx

=

A)

B)

C)

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




D)

E)

5. Find all zeros of the function ( )( )2 3( ) – 2 – 216f x x x x= .

A) 2,216x = B) 0, –2, –6x = C) 0,2,6, –3 3 3 , –3 3 3x i i= − + D) –2, –216x = E) 0,2,6x =

6. Simplify ( )9–3 and write the answer in standard form.

A) –81 3 i B) 81 3 i C) 6561 3 i D) 81 3 E) The expression cannot be simplified.

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




7. Write the complex conjugate of the following complex number and then multiply the

number by the complex conjugate. Write the result in standard form. 2 –27+ A) 2 – 27 i ; 25 B) 2 3 3 i− ; 31 C) –2 3 3 i− ; 31 D) –2 3 3 i− ; 25 E) 2 3 3 i− ; 31

8. Determine the x-intercept(s) of the quadratic function 2( ) + 6 + 10f x x x= . A) ( ) ( )–8,0 , 1,0

B) ( ) ( )–3,0 , 7,0

C) ( ) ( )–1,0 , –6,0

D) ( ) ( )–8,0 , –6,0 E) no x-intercept(s)

9. Compare the graph of ( )21( ) – + 9 – 9

3p x x⎡ ⎤= ⎢ ⎥⎣ ⎦

with 2( )p x x= .

A) ( )

21( ) – + 9 – 93

p x x⎡ ⎤= ⎢ ⎥⎣ ⎦ shifts right 9 units, shifts downward 9 units, and shrinks

by a factor of 19

− .

B) ( )

21( ) – + 9 – 93

p x x⎡ ⎤= ⎢ ⎥⎣ ⎦ shifts right 81 units, shifts upward 9 units, and shrinks

by a factor of 19

.

C) ( )

21( ) – + 9 – 93

p x x⎡ ⎤= ⎢ ⎥⎣ ⎦ shifts left 9 units, shifts downward 9 units, and shrinks

by a factor of 19

.

D) ( )

21( ) – + 9 – 93

p x x⎡ ⎤= ⎢ ⎥⎣ ⎦ shifts right 9 units, shifts upward 9 units, and shrinks by

a factor of 19

.

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




E) ( )

21( ) – + 9 – 93

p x x⎡ ⎤= ⎢ ⎥⎣ ⎦ shifts left 81 units, shifts upward 9 units, and shrinks by

a factor of 13

− .

10. Find a polynomial function of the lowest degree with real coefficients that has the zeros below and whose leading coefficient is one.

0, 2, 4 – i A) ( ) 4 3 2– 34 + 32 –10f x x x x x=

B) ( ) 4 3 2–10 + 33 – 34f x x x x x=

C) ( ) 4 3 2+ 32 –10 – 34f x x x x x=

D) ( ) 4 3 2–10 – 34 + 32f x x x x x=

E) ( ) 4 3 2+ 32 – 34 –10f x x x x x=

11. If –1x = is a root of 3 2 + 2 – – 2 0x x x = , use synthetic division to factor the polynomial completely and list all real solutions of the equation. A) ( )( )( ) – 2 + 1 – 1x x x ; 2, –1, 1x =

B) ( )( )( ) + 2 + 1 – 1x x x ; –2, –1, 1x =

C) ( )( )2 + 2 + 1x x ; –2, –1x =

D) ( ) ( )2 + 2 + 1x x ; –2, –1x =

E) ( )( )( ) + 2 – 2 – 1x x x ; –2, 2, 1x =

12. Determine the vertex of the graph of the quadratic function 2( ) + 5f x x= . A) ( )0, –5

B) ( )5,0

C) ( )5,5

D) ( )0,5

E) ( )–5,0

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




13. Find all real zeros of the polynomial 4 2( ) – 80 + 1024f x x x= and determine the mutiplicity of each. A) 64x = , multiplicity 2; 16x = , multiplicity 2 B) 8x = , multiplicity 2; 4x = , multiplicity 2 C) 64x = , multiplicity 2; 4x = , multiplicity 1 D) –8x = , multiplicity 2; –4x = , multiplicity 2

E) 8x = , multiplicity 1; –8x = , multiplicity 1; 4x = , multiplicity 1; –4x = , multiplicity 1


2( ) 5+ 5

g xx

= + .

A) 5, 5x x= − = B) –2x =

C) 2 2– ,5 5

x x= =

D) x = –5, x = 5 E) no zeros

15. Use the regression feature of a graphing utility to find a quadratic model for the data below.

x y −2 –7.3 −1 –2 0 –1 1 –4.8 2 –11.4 3 –22.8 4 –37.8

A) 2–1.91 –1.21 –1.57y x x= B) 2–1.81 –1.15 –1.42y x x= C) 2–2.21 –1.04 –1y x x= D) 2–2.11 – 0.99 –1.07y x x= E) 2–2.01 –1.1 –1.28y x x=

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.





A)

B)

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




C)

D)

E)

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




17. Simplify 1 – 25

ii


A) 2 –5 5

i

B) 2– –5 5

i

C) 2– +5 5

i

D) 1 2–5 5

i

E) 1 2– –5 5

i

18. Use long division to divide. ( ) ( )26 – 20 + 6 – 3x x x÷

A) 1206 – 38 + – 3

xx

B) 6 – 2x

C) 406 – 38 + – 3

xx

D) 6 – 40x E) –6 + 2x

19. Compare the graph of ( )2( ) 5 – 5 + 9s x x= with 2( )s x x= .

A) ( )2( ) 5 – 5 + 9s x x= shifts right 5 units, shifts downward 9 units, and shrinks by a

factor of 15

.

B) ( )2( ) 5 – 5 + 9s x x= shifts right 5 units, shifts upward 9 units, and stretches by a factor of 5 .

C) ( )2( ) 5 – 5 + 9s x x= shifts left 5 units, shifts downward 9 units, and stretches by a factor of 5 .

D) ( )2( ) 5 – 5 + 9s x x= shifts right 5 units, shifts upward 9 units, and shrinks by a

factor of 15

.

E) ( )2( ) 5 – 5 + 9s x x= shifts left 5 units, shifts upward 9 units, and stretches by a factor of 5 .

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.





( ) 6 3+ 28 + 27f x x x= A) –3 and –1 B) –2 and –1 C) –3 and –2 D) –2, –1, 1, and 2 E) –3, –2, 2, and 3

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




Answer Key

1. C 2. A 3. B 4. E 5. C 6. B 7. E 8. E 9. C

10. B 11. B 12. D 13. E 14. E 15. E 16. D 17. B 18. B 19. B 20. A

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




Name: __________________________ Date: _____________

1. Given 2

5 + 4( )5 + 4

xf xx x

= . Determine the domain of ( )f x and find any vertical

asymptotes.

A) domain: all real numbers except 4–5

x =

vertical asymptote: 0x =

B) domain: all real numbers except 40 and –5

x x= =


C) domain: all real numbers

vertical asymptotes: 40 and –5

x x= =

D) domain: all real numbers except 40 and 5

x x= =


E) domain: all real numbers except 4

5x =

vertical asymptotes: 40 and –5

x x= =

2. Determine the value that 3 5( )6

xf xx

−=−

approaches as x increases and decreases in

magnitude without bound. A) 6 B) 5 C) 4 D) 3 E) 2


B) ( ) ( )–4,0 , –8,0

C) ( ) ( )–8,0 , –7,0


Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




4. Simplify 2 + 5 + 2

ii


A) 12 1– +29 29

i

B) 12 1–29 29

i

C) 12 1+29 29

i

D) 1 12+29 29

i

E) 1 12–29 29

i

5. Write the polynomial in completely factored form. (Hint: One factor is 2 1.x + )

( ) 4 3 2+ 6 +14 + 6 +13f x x x x x=

A) ( ) ( )( )( )( )– 2 + 2 + 3 – + 3 +f x x x x i x i=

B) ( ) ( )( )( )( )– 3 + 3 –1– 2 –1+ 2f x x x x i x i=

C) ( ) ( )( )( )( )–1 +1 + 3 – 2 + 3 + 2f x x x x i x i=

D) ( ) ( )( )( )( )– 3 + 3 –1– 2 –1+ 2f x x i x i x i x i=

E) ( ) ( )( )( )( )– + + 3 – 2 + 3+ 2f x x i x i x i x i=

6. Use long division to divide. ( ) ( )3 2 + 5 + 36 + 180 + 5x x x x÷

A) 2 + 30x

B) 2 244 + 10 + 44 + 5

x xx

−

C) 2 110 + 10 + 86 + 5

x xx

+

D) 2 + 10 + 44x x E) 2 + 36x

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




7. Find the quadratic function f whose graph intersects the x-axis at ( )–7,0 and ( )1,0 and

the y-axis at ( )0, –14 .

A) ( ) 2–2 –16 – 2f x x x=

B) ( ) 22 +12 –14f x x x=

C) ( ) 22 +16 – 7f x x x=

D) ( ) 2–2 +16 –14f x x x=

E) ( ) 2–2 –12 –14f x x x=

8. Suppose the IQ scores (y, rounded to the nearest 10) for a group of people are summarized in the table below. Use the regression feature of a graphing utility to find a quadratic function of the form 2y ax bx c= + + for the data.

IQ Score y

Number of People x

70 53 80 72 90 93 100 90 110 78 120 47 130 16

A) 2–0.04 +14.93 – 404.96y x x= B) 2–0.06 +11.94 – 476.43y x x= C) 2–0.08 +10.87 – 500.25y x x= D) 2–0.07 +13.5 – 452.61y x x= E) 2–0.09 +8.48 – 547.89y x x=

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.





A)

B)

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




C)

D)

E)

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




10. Use the regression feature of a graphing utility to find a quadratic model for the data

below.

x y −2 15.7 −1 3.5 0 –2.7 1 –2.9 2 3.7 3 15.8 4 33.6

A) 22.89 – 3.35 – 2.9y x x= B) 22.73 – 3.2 – 2.75y x x= C) 23.34 – 2.9 – 2.7y x x= D) 23.19 – 2.74 – 2.4y x x= E) 23.04 – 3.05 – 2.61y x x=


( )2 –1– xf xx

=

A)

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




B)

C)

D)

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




E)

12. If 2( ) 4 – 2 – 7f x x x= , use synthetic division to evaluate 78

f ⎛ ⎞⎜ ⎟⎝ ⎠

.

A) 7 218 2

f ⎛ ⎞ =⎜ ⎟⎝ ⎠

B) 7 21–8 2

f ⎛ ⎞ =⎜ ⎟⎝ ⎠

C) 7 91–8 16

f ⎛ ⎞ =⎜ ⎟⎝ ⎠

D) 7 35–8 2

f ⎛ ⎞ =⎜ ⎟⎝ ⎠

E) 7 77–8 8

f ⎛ ⎞ =⎜ ⎟⎝ ⎠

13. Find a polynomial function of the lowest degree with real coefficients that has the zeros below and whose leading coefficient is one.

0, –3, 1+ 3i A) ( ) 4 3 2+ 30 – 5 +f x x x x x=

B) ( ) 4 3 2+ + 4 + 30f x x x x x=

C) ( ) 4 3 2– 5 + + 30f x x x x x=

D) ( ) 4 3 2+ + 30 – 5f x x x x x=

E) ( ) 4 3 2– 5 + 30 +f x x x x x=

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




14. Simplify ( )( )–4 4 – 5i i+ and write the answer in standard form. A) 16 + 24 i B) –11 – 24 i C) –16 + 24 i D) –16 – 21i E) –11 + 24 i

15. Write the standard form of the equation of the parabola that has a vertex at 2 1,3 9

−⎛ ⎞⎜ ⎟⎝ ⎠

and

passes through the point ( )3, –4 .

A) 237 2 1( ) –

11 3 9f x x⎛ ⎞= + +⎜ ⎟

⎝ ⎠

B) 237 3 1( ) –

121 2 9f x x⎛ ⎞= − +⎜ ⎟

⎝ ⎠

C) 237 2 1( ) –

121 3 9f x x⎛ ⎞= + +⎜ ⎟

⎝ ⎠

D) 237 2 1( ) –

11 3 9f x x⎛ ⎞= − −⎜ ⎟

⎝ ⎠

E) 237 3 1( ) –

25 2 9f x x⎛ ⎞= − −⎜ ⎟

⎝ ⎠

16. Determine the vertex of the graph of the quadratic function 2 29( ) + 5 +4

f x x x= .

A) –5 27,2 2

⎛ ⎞⎜ ⎟⎝ ⎠

B) 295,4

⎛ ⎞⎜ ⎟⎝ ⎠

C) 5 29,2 4

⎛ ⎞⎜ ⎟⎝ ⎠

D) 5 21,4 4

⎛ ⎞⎜ ⎟⎝ ⎠

E) –5 ,12

⎛ ⎞⎜ ⎟⎝ ⎠

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




17. Use synthetic division to divide. ( ) ( )3 26 + 5 + 23 + 22 + 3x x x x÷

A) 25 + 8 + 3x x B) 25 + 17 + 10x x C) 25 + 5 + 6x x D) 25 + 7 + 2x x E) 25 + 7 + 5x x


41 27( )6 2

f t t= −

A) –3, –1, 1, and 3 B) –3 and 3 C) –6 and 6 D) –6, –1, 1, and 6 E) No zeros exist.

19. Find real numbers a and b such that the equation 4 – 9a bi i+ = is true. A) –4, 9a b= = B) 4, 9a b= = C) –4, –9a b= = D) 4, –9a b= = E) 13, –5a b= =

20. Determine the vertex of the graph of the quadratic function 2( ) + 2f x x= . A) ( )0, –2

B) ( )2,0

C) ( )2, 2

D) ( )0, 2

E) ( )–2,0

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.




Answer Key

1. B 2. D 3. A 4. C 5. E 6. E 7. B 8. B 9. D

10. E 11. E 12. C 13. B 14. E 15. C 16. E 17. D 18. B 19. D 20. D

Not For Sale

© 2

014

Cen

gage

Lea

rnin

g. A

ll R

ight

s Res

erve

d. T

his c

onte

nt is

not

yet

fina

l and

Cen

gage

Lea

rnin

g do

es n

ot g

uara

ntee

this

pag

e w

ill c

onta

in c

urre

nt m

ater

ial o

r mat

ch th

e pu

blis

hed

prod

uct.

Precalculus with Limits A Graphing Approach Texas Edition 6th Edition Larson Test BankFull Download: http://testbanklive.com/download/precalculus-with-limits-a-graphing-approach-texas-edition-6th-edition-larson-test-bank/

Full download all chapters instantly please go to Solutions Manual, Test Bank site: testbanklive.com

http://testbanklive.com/download/precalculus-with-limits-a-graphing-approach-texas-edition-6th-edition-larson-test-bank/

Chapter 2: Polynomial and Rational Functions...Larson’s Precalculus with Limits: A Graphing...

Documents

Transcript of Chapter 2: Polynomial and Rational Functions...Larson’s Precalculus with Limits: A Graphing...