Name: ______________________ Class: _________________ Date: _________ ID: A

1

Polynomial and Rational Functions (Ch. 2) Test Review

____ 1. The height y (in feet) of a punted football is given by

y = -16

2025x2 +

9

5x + 1.8

where x is the horizontal distance (in feet) from the point at which the ball is punted.What is the maximum height of the punt? (Round your answer to two decimal places.)

a. 114.32 b. 124.32c. 104.32d. 134.32e. 144.32

____ 2. Which of the following is an equation for the quadratic function shown below?

a. f x( ) = - x + 1( ) 2 + 3

b. f x( ) = - 34

x + 1( ) 2 + 3

c. f x( ) = - 1 - x( ) 2 + 3

d. f x( ) = - 34

x - 1( ) 2 + 3

e. f x( ) = - 14

x + 1( ) 2 + 3

Name: ______________________ ID: A

2

____ 3. From the graph of the quadratic function f x( ) = x + 5( ) 2 - 1, determine the equation of the axis of symmetry.a. x = - 1b. x = - 5

c. x = - 15

d. x = 5e. x = 1

____ 4. Determine the x-intercept(s) of the quadratic functionf x( ) = x2 + 4x + 5.a. no x-intercept(s)b. -1, 0Ê

ËÁÁˆ¯̃̃ , -6, 0Ê

ËÁÁˆ¯̃̃

c. -3, 0ÊËÁÁ

ˆ¯̃̃ , 4, 0Ê

ËÁÁˆ¯̃̃

d. -8, 0ÊËÁÁ

ˆ¯̃̃ , -6, 0Ê

ËÁÁˆ¯̃̃

e. -8, 0ÊËÁÁ

ˆ¯̃̃ , -2, 0Ê

ËÁÁˆ¯̃̃

____ 5. Determine the vertex of the graph of the quadratic function f x( ) = x2 - 3x + 134

.

a. 32

, 1Ê

Ë

ÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜

b. 32

, 112

Ê

Ë

ÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜

c. - 34

, 54

Ê

Ë

ÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜

d. -3, 134

Ê

Ë

ÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜

e. - 32

, 134

Ê

Ë

ÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜

Name: ______________________ ID: A

3

____ 6. Select the graph of y = x3 and the transformation f x( ) = x - 4( )3 .

a. d.

b. e.

c.

Name: ______________________ ID: A

4

____ 7. Select the correct description of the end behavior of the graph of the polynomial function.

f x( ) =1

2x3 + 4x

a. Rises to the right, rises to the leftb. Rises to the left, falls to the rightc. Falls to the left, falls to the rightd. Falls to the righte. Falls to the left, rises to the right

____ 8. Determine the multiplicity of each zero and the number of turning points of the graph of thefunction.

h t( ) = t2 - 10t + 25

a. Odd multiplicity; number of turning points: 2b. Even multiplicity; number of turning points: 1c. Even multiplicity; number of turning points: 3d. Even multiplicity; number of turning points: 2e. Odd multiplicity; number of turning points: 1

____ 9. Select from the following which is the polynomial function that has the given zeros.

1 + 7 ,1 - 7

a. f x( ) = x2 - 2x + 6

b. f x( ) = -x2 - 2x + 6

c. f x( ) = x2 - 2x - 6

d. f x( ) = -x2 - 2x - 6

e. f x( ) = x2 + 2x - 6

Name: ______________________ ID: A

5

____ 10. Match the equation with its graph.

f x( ) = x3 + x2 - 6x4

a. d.

b. e.

c.

____ 11. Describe the end behavior of the graph of r x( ) = - 6x4 + 7x3 - 22.a. Because the degree is odd and the leading coefficient is negative, the graph rises to

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

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

the left and falls to the right.d. Because the degree is even and the leading coefficient is negative, 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 falls to

the left and falls to the right.

Name: ______________________ ID: A

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____ 12. Find the zeros of f x( ) = x3 - 49x and each of the zero’s multiplicity.a. x = 0, multiplicity 3b. x = 0, multiplicity 2; x = - 7, multiplicity 1c. x = 7, multiplicity 2; x = - 7, multiplicity 1d. x = 0, multiplicity 1; x = 7, multiplicity 2e. x = 0, multiplicity 1; x = 7, multiplicity 1; x = - 7, multiplicity 1

____ 13. Use long division or synthetic division to divide the following.

x4 + 10x3 + 25x2 - x - 5Ê

ËÁÁÁÁ

ˆ

¯˜̃̃˜ ∏ x + 5( )

a. x3 + 5x2 - 1b. x3 + 5x2 + 1c. x3 - 5x2 - 1d. x3 - 5x2 + 1e. x3 + 5x2 + 1

____ 14. Find the value of k such that

x - 4 is a factor of x3 - kx2 + 2kx - 8.

a. k = 8b. k = 7c. k = 5d. k = 6e. k = 9

____ 15. Use the Remainder Theorem and synthetic division to find the function value.

h(x) = x3 - 6x2 - 6x + 6, h(-7)

a. –589b. –588c. –591d. –585e. –587

Name: ______________________ ID: A

7

____ 16. Using the factors 5x + 2( ) and x - 1( ) , find the remaining factor(s) of

f x( ) = - 10x4 + 61x3 - 54x2 - 7x + 10 and write the polynomial in fully factored form.

a. f x( ) = 5x + 2( ) 2 x - 1( ) 2

b. f x( ) = 5x + 2( ) 5x + 2( ) 2x - 1( ) x - 1( )

c. f x( ) = 5x + 2( ) 2 2x - 1( ) x + 1( )

d. f x( ) = 5x + 2( ) -x + 5( ) 2x - 1( ) x - 1( )

e. f x( ) = 5x + 2( ) -x - 5( ) 2 x + 1( )

____ 17. Write the complex number in standard form.

5 + -9

a. 5 + 3ib. 8 - 6ic. 5 + 9id. 8 + 6ie. 5 - 3i

____ 18. Write the complex number in standard form.

-17i + i2

a. -1 + 17ib. -1 - 17ic. 1 - 17id. 1 + 17ie. -1 - 20i

____ 19. Perform the addition or subtraction and write the result in standard form.

11 - i( ) - 7 - i( )

a. 8b. 4c. 5d. 7e. 6

Name: ______________________ ID: A

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____ 20. Perform the operation and write the result in standard form.

1 + i( ) 4 - 3i( )

a. 11 + ib. 9 + ic. 10 + id. 7 + ie. 8 + i

____ 21. Write the complex conjugate of the complex number. Then multiply the number by its complex conjugate.

7 + 4i

a. 7 - 4i, 65b. -7 - 4i, 65c. 7 + 4i, 16d. 7 + 4i, 65e. 7 - 4i, 16

____ 22. Find all the zeros of the function.

x - 3( ) x + 9( )3

a. -3,9b. 3,9c. -3,3,- 9d. -3,- 9e. 3,- 9

Name: ______________________ ID: A

9

____ 23. Select the graph of f.

f x( ) = x3 + x2 - x - 1

a. d.

b. e.

c.

Name: ______________________ ID: A

10

____ 24. Find a polynomial function with real coefficients that has the given zeros.

5,6 + 2i a. x3 - 17x2 - 100x - 200b. x3 + 17x2 + 100x + 200c. x3 - 17x2 + 100x - 200d. x3 - 17x2 + 100x + 200e. x3 + 17x2 + 100x - 200

____ 25. Write f x( ) = x3 + 2x2 + 9x + 18 as a product of linear factors.a. x = x + 2( ) x + 3i( ) x - 3i( )

b. x = x - 2( ) x + 3( ) 2

c. x = x + 2( ) x - 2( ) x + 3( )

d. x = x - 2( ) 2 x - 3i( )

e. x = x - 2( ) x - 3( ) 2

Name: ______________________ ID: A

11

____ 26. Select the correct rational function for the following graph.

a. f x( ) =4

x - 4

b. f x( ) =3

x - 4

c. f x( ) =4

x - 3

d. f x( ) =3

x + 4

e. f x( ) =3

x + 3____ 27. Find vertical asymptotes of the following function.

g x( ) =x - 6

x2 - 36

a. x = 0b. x = 36c. x = -36d. x = 6e. x = -6

Name: ______________________ ID: A

12

____ 28. Find domain of the following function.

g x( ) =1

x + 5

a. all real numbers x except x = 5 b. all real numbers x except x = 1c. all real numbers x except x = -5d. all real numbers x except x = -1e. all real numbers x except x = 25

____ 29. Find all intercepts of the following function.

g x( ) = 1x - 3

a. x-intercept: -1

3, 0

Ê

Ë

ÁÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃̃˜

b. y-intercept: 0, -1

3

Ê

Ë

ÁÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃̃˜

c. x-intercept: -1

3, 0

Ê

Ë

ÁÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃̃˜ and y-intercept: 0, -

1

3

Ê

Ë

ÁÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃̃˜

d. x-intercept: 1

3, 0

Ê

Ë

ÁÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃̃˜

e. y-intercept: 0,1

3

Ê

Ë

ÁÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃̃˜

Name: ______________________ ID: A

13

____ 30. Find vertical and horizontal asymptotes.

f x( ) =1

x - 8

a. Vertical asymptote: x = 8Horizontal asymptote: y = 0

b. Vertical asymptote: x = 0Horizontal asymptote: y = 8

c. Vertical asymptote: x = 0Horizontal asymptote: y = -8

d. Vertical asymptote: x = -8Horizontal asymptote: y = 1

e. Vertical asymptote: x = -8Horizontal asymptote: y = 0

____ 31. Determine the equations of the vertical and horizontal asymptotes of the graph of the function

f x( ) = 5x2

x2 - 16.

a. horizontal: y = 5; vertical: x = 4 and x = - 4b. horizontal: y = - 4; vertical: x = 5c. horizontal: y = 5; vertical: x = 4d. horizontal: x = - 5; vertical: y = 4 and y = - 4e. horizontal: x = 4 and x = - 4; vertical: y = - 5

____ 32. Determine the zeros (if any) of the rational function f x( ) = x2 - 64x + 5

.

a. x = - 64, x = 64b. x = - 8, x = 8

c. x = - 85

, x = 85

d. no zerose. x = - 5

____ 33. Given f x( ) = x2 - 7x - 1x - 6

, determine the equations of any slant and vertical asymptote.

a. slant: y = x + 5; vertical: x = - 7b. slant: y = x - 1; vertical: x = 6c. slant: none; vertical: noned. slant: y = x + 1; vertical: x = - 1e. slant: y = x - 13; vertical: none

ID: A

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Polynomial and Rational Functions (Ch. 2) Test ReviewAnswer Section

1. ANS: C PTS: 1 REF: 2.1.76b 2. ANS: B PTS: 1 REF: 2.1.7

OBJ: Determine the standard form of a quadratic function 3. ANS: B PTS: 1 REF: 2.1.23 OBJ: Determine axis of symmetry 4. ANS: A PTS: 1 REF: 2.1.26

OBJ: Determine x-intercepts of quadratic function 5. ANS: A PTS: 1 REF: 2.1.27

OBJ: Determine vertex of quadratic function 6. ANS: D PTS: 1 REF: 2.2.17a 7. ANS: E PTS: 1 REF: 2.2.21 8. ANS: B PTS: 1 REF: 2.2.37b 9. ANS: C PTS: 1 REF: 2.2.63 10. ANS: E PTS: 1 REF: 2.2.16 OBJ: Match polynomial and graph 11. ANS: E PTS: 1 REF: 2.2.22

OBJ: Determine right/left-hand behavior of polynomial 12. ANS: E PTS: 1 REF: 2.2.75

OBJ: Approximate roots with graphing utility 13. ANS: A PTS: 1 REF: 2.3.15 14. ANS: B PTS: 1 REF: 2.3.97 15. ANS: A PTS: 1 REF: 2.3.57c 16. ANS: D PTS: 1 REF: 2.3.70 OBJ: Factor polynomial given factor(s) 17. ANS: A PTS: 1 REF: 2.4.9 18. ANS: B PTS: 1 REF: 2.4.17 19. ANS: B PTS: 1 REF: 2.4.23 20. ANS: D PTS: 1 REF: 2.4.31 21. ANS: A PTS: 1 REF: 2.4.41 22. ANS: E PTS: 1 REF: 2.5.11 23. ANS: B PTS: 1 REF: 2.5.33b 24. ANS: C PTS: 1 REF: 2.5.48 25. ANS: A PTS: 1 REF: 2.5.74

OBJ: Approximate zeros with graphing utility 26. ANS: D PTS: 1 REF: 2.6.17 27. ANS: E PTS: 1 REF: 2.6.25b 28. ANS: C PTS: 1 REF: 2.6.31a 29. ANS: B PTS: 1 REF: 2.6.32b 30. ANS: A PTS: 1 REF: 2.6.34c 31. ANS: A PTS: 1 REF: 2.6.13

OBJ: Determine vertical and horizontal asymptotes 32. ANS: B PTS: 1 REF: 2.6.21

OBJ: Determine zeros of a rational function 33. ANS: B PTS: 1 REF: 2.6.65c

OBJ: Determine equation of slant asymptote