Polynomial And Rational Functions Ch4 Complete Test Bank - Test Bank | College Algebra 5e by Young by Cynthia Y. Young. DOCX document preview.

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Polynomial And Rational Functions Ch4 Complete Test Bank

College Algebra, 5e (Young)

Chapter 4 Polynomial and Rational Functions

4.2 Polynomial Functions of Higher Degree

1) Determine if the function f (x) = 21(x) with superscript (42) + 30(x) with superscript (30) - 30(x) with superscript (21) + 49 is a polynomial. If it is, state the degree.

A) Not a polynomial

B) a polynomial of degree 21

C) a polynomial of degree 42

D) a polynomial of degree 4

Diff: 1 Var: 1

Chapter/Section: Ch 04, Sec 02

Learning Objective: Identify a polynomial function and determine its degree.

2) Determine if the function f (x) = (2/(x) with superscript (39)) + 38(x) with superscript (17) - 25 is a polynomial. If it is, state the degree.

A) Not a polynomial

B) a polynomial of degree 17

C) a polynomial of degree 39

D) a polynomial of degree -39

Diff: 1 Var: 1

Chapter/Section: Ch 04, Sec 02

Learning Objective: Identify a polynomial function and determine its degree.

3) Determine if the function f (x) = 7((x + 43)) with superscript (18)((x - 12)) with superscript (6)(x + 31) is a polynomial. If it is, state the degree.

A) Not a polynomial

B) a polynomial of degree 18

C) a polynomial of degree 7

D) a polynomial of degree 25

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 02

Learning Objective: Identify a polynomial function and determine its degree.

4) Find all the real zeros (and state their multiplicity) of the polynomial function.

y = 2(x) with superscript (4)(x + 7)(x - 1)

A) 0, -7, 1

B) -7, 1

C) 0 (multiplicity 4), -7, and 1

D) 0 (multiplicity 4), 7, and -1

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 02

Learning Objective: Identify real zeros of a polynomial function and their multiplicities.

5) Find all the real zeros (and state their multiplicity) of the polynomial function.

y = x((x - 1)) with superscript (2)((x) with superscript (2) + 20)

A) 0, 1 (multiplicity 2)

B) 0, -1, (multiplicity 2)

C) 1, 1, (multiplicity 2), 20 (multiplicity 2)

D) 0, 1 (multiplicity 2), (20) to the ( ) root

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 02

Learning Objective: Identify real zeros of a polynomial function and their multiplicities.

6) Find all the real zeros (and state their multiplicity) of the polynomial function.

y = (x) with superscript (6) - 16(x) with superscript (5) + 64(x) with superscript (4)

A) 0, 8

B) 0 (multiplicity 4), 8 (multiplicity 2)

C) 8 (multiplicity 2)

D) 0 (multiplicity 6), 8 (multiplicity 2)

Diff: 3 Var: 1

Chapter/Section: Ch 04, Sec 02

Learning Objective: Identify real zeros of a polynomial function and their multiplicities.

7) Find a polynomial of minimum degree with zeros 4, -3 and 5 (of multiplicity 2).

A) y = (x) with superscript (4) + 11(x) with superscript (3) + 23(x) with superscript (2) - 95x - 300

B) y = (x) with superscript (3) - 6(x) with superscript (2) - 7x + 60

C) y = (x) with superscript (4) - (x) with superscript (3) + 13(x) with superscript (2) - 25x -300

D) y = (x) with superscript (4) - 11(x) with superscript (3) + 23(x) with superscript (2) + 95x - 300

Diff: 3 Var: 1

Chapter/Section: Ch 04, Sec 02

Learning Objective: Identify real zeros of a polynomial function and their multiplicities.

8) Find a polynomial of minimum degree that has zeros -9, 0 (multiplicity 2) and 7.

A) y = (x) with superscript (4) + 2(x) with superscript (3) - 63(x) with superscript (2)

B) y = (x) with superscript (2) - 2x - 63

C) y = (x) with superscript (4) - 2(x) with superscript (4) - 63(x) with superscript (2)

D) y = (x) with superscript (2) + 2x - 63x

Diff: 3 Var: 1

Chapter/Section: Ch 04, Sec 02

Learning Objective: Identify real zeros of a polynomial function and their multiplicities.

9) Find a polynomial of minimum degree with zeros 0, 10 + square root of (10), and 10 - square root of (10).

A) y = (x) with superscript (2) - 20x + 90

B) y = (x) with superscript (3) + 20(x) with superscript (2) + 90x

C) y = (x) with superscript (3) - 20(x) with superscript (2) + 90x

D) y = (x) with superscript (2) + 20x + 90

Diff: 4 Var: 1

Chapter/Section: Ch 04, Sec 02

Learning Objective: Identify real zeros of a polynomial function and their multiplicities.

10) Find a polynomial of minimum degree that has the zeros square root of (5) (with multiplicity 2) and -square root of (5) (with multiplicity 2).

A) f (x) = (x) with superscript (4) + 10(x) with superscript (2) + 25

B) f (x) = (x) with superscript (4) - 10(x) with superscript (2) + 25

C) f (x) = (x) with superscript (4) + 25

D) f (x) = (x) with superscript (2) + 10x + 25

Diff: 4 Var: 1

Chapter/Section: Ch 04, Sec 02

Learning Objective: Identify real zeros of a polynomial function and their multiplicities.

11) For the polynomial function y = (x - 12)((x + 16)) with superscript (30)(x - 14), determine whether the graph touches or crosses at the x - intercept (-16, 0).

A) crosses the y - axis at (-16, 0)

B) touches the y - axis at (-16, 0)

C) crosses the x - axis at (-16, 0)

D) touches the x - axis at (-16, 0)

Diff: 1 Var: 1

Chapter/Section: Ch 04, Sec 02

Learning Objective: Graph polynomial functions: x-intercepts; multiplicity (touch/cross) of each zero; end behavior.

12) For the polynomial function f (x) = (x) with superscript (11)((x + 14)) with superscript (6)(x - 14), determine whether the graph touches or crosses at the x-intercept (0, 0).

A) touches the x-axis at (0, 0)

B) crosses the x-axis at (0, 0)

C) touches the x-axis at (14, 0)

D) neither

Diff: 1 Var: 1

Chapter/Section: Ch 04, Sec 02

Learning Objective: Graph polynomial functions: x-intercepts; multiplicity (touch/cross) of each zero; end behavior.

13) For the polynomial function f (x) = x((x + 9)) with superscript (6)(x - 1), find the y-intercept.

A) (1, 0)

B) (-1, 0)

C) (0, 0)

D) (0, 1)

Diff: 1 Var: 1

Chapter/Section: Ch 04, Sec 02

Learning Objective: Graph polynomial functions: x-intercepts; multiplicity (touch/cross) of each zero; end behavior.

14) For the polynomial function f (x) = (x - 6)(x + 4)((x - 2)) with superscript (2), find the y-intercept.

A) (0, -48)

B) (0, -96)

C) (0, 48)

D) (0, 2)

Diff: 1 Var: 1

Chapter/Section: Ch 04, Sec 02

Learning Objective: Graph polynomial functions: x-intercepts; multiplicity (touch/cross) of each zero; end behavior.

15) Determine if the function f (x) = 7((x - 3)) with superscript (9)((x + 7)) with superscript (4)(x - 7) is a polynomial. If it is, state the degree.

Diff: 1 Var: 1

Chapter/Section: Ch 04, Sec 02

Learning Objective: Identify a polynomial function and determine its degree.

16) Find all the real zeros (and state their multiplicity) of the polynomial function.

f (x) = (-5) with superscript (3)((x - 5)) with superscript (10)((x + 16)) with superscript (2)](x - 20)

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 02

Learning Objective: Identify real zeros of a polynomial function and their multiplicities.

17) Find a polynomial of minimum degree that has the zeros square root of (2) (with multiplicity 2) and -square root of (2) (with multiplicity 2).

Diff: 4 Var: 1

Chapter/Section: Ch 04, Sec 02

Learning Objective: Identify real zeros of a polynomial function and their multiplicities.

18) Sketch the graph of the polynomial function.

f of x equals negative 2 times x cubed left parenthesis x minus 2 right parenthesis left parenthesis x plus 3 right parenthesis.

A curve is graphed on an x y coordinate plane. The x axis ranges from negative 6 to 4, in increments of 0.5. The y axis ranges from negative 75 to 37.5, in increments of 12.5. The curve decreases concave up through (negative 3, 0) to (negative 2.5, negative 75) and increases concave down to (0, 0). It then increases concave down to (1.5, 12.5) and decreases concave down through (2, 0) to (2.5, negative 75) into the fourth quadrant. All values are estimated.

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 02

Learning Objective: Graph polynomial functions: x-intercepts; multiplicity (touch/cross) of each zero; end behavior.

19) Sketch the graph of the polynomial function.

f of x equals x cubed plus 2 times x squared.

A curve is graphed on an x y coordinate plane. The x axis ranges from negative 4 to 2, in increments of 0.5. The y axis ranges from negative 4 to 4, in increments of 0.5. The curve increases concave down through (negative 2.8, negative 4) and (negative 2, 0) to (negative 1.5, 1.5) and decreases concave down to (0, 0). It then increases concave up through (1, 2.5) to (1.2, 4) into the first quadrant. All values are estimated.

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 02

Learning Objective: Graph polynomial functions: x-intercepts; multiplicity (touch/cross) of each zero; end behavior.

20) Match the polynomial function with its graph.

f of x equals x left parenthesis x minus 3 right parenthesis left parenthesis x plus 4 right parenthesis.

A)

A curve is graphed on an x y coordinate plane. The x axis ranges from negative 6 to 5, in increments of 0.5. The y axis ranges from negative 20 to 50, in increments of 5. The curve increases concave down through (negative 4.8, negative 20) and (negative 4, 0) to (negative 2.5, 20) and decreases concave down through (0, 0) to (1.8, negative 10). It then increases concave up through (3, 0) to (4.5, 45) into the first quadrant. All values are estimated.

B)

A curve is graphed on an x y coordinate plane. The x axis ranges from negative 6 to 5, in increments of 0.5. The y axis ranges from negative 50 to 20, in increments of 5. The curve decreases concave up through (negative 4.8, 20) and (negative 4, 0) to (negative 2.5, negative 20) and increases concave up through (0, 0) to (1.5, 15). It then decreases concave down through (3, 0) to (4.8, negative 50) into the fourth quadrant. All values are estimated.

C)

A curve is graphed on an x y coordinate plane. The x axis ranges from negative 5 to 6, in increments of 0.5. The y axis ranges from negative 50 to 20, in increments of 5. The curve increases concave down through (negative 4.5, negative 45) and (negative 3, 0) to (negative 2, 15). It then decreases concave down through (0, 0) to (2.5, negative 20) and increases concave up through (4, 0) to (4.6, 20) into the first quadrant. All values are estimated.

D)

A curve is graphed on an x y coordinate plane. The x axis ranges from negative 5 to 6, in increments of 0.5. The y axis ranges from negative 20 to 50, in increments of 5. The curve decreases concave up through (negative 4.5, 50) and (negative 3, 0) to (negative 2, negative 15) and increases concave up through (0, 0) to (2.5, 25). It then decreases concave down through (4, 0) to (4.6, negative 20) into the fourth quadrant. All values are estimated.

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 02

Learning Objective: Graph polynomial functions: x-intercepts; multiplicity (touch/cross) of each zero; end behavior.

21) Match the polynomial function with its graph.

f of x equals 4 times x cubed plus 12 times x squared plus 9 times x.

A)

A curve is graphed on an x y coordinate plane. The x axis ranges from negative 4 to 2, in increments of 0.5. The y axis ranges from negative 6 to 6, in increments of 1. The curve increases concave down through (negative 2.5, negative 4) to (negative 1.5, 0) and decreases concave down to (negative 0.5, negative 2). It then increases concave up through (0, 0) to (0.5, 4) into the first quadrant. All values are estimated.

B)

A curve is graphed on an x y coordinate plane. The x axis ranges from negative 4 to 2, in increments of 0.5. The y axis ranges from negative 6 to 6, in increments of 1. The curve decreases concave up through (negative 2.5, 5) to (negative 1.5, 0) and increases concave up to (negative 0.5, 2). It then decreases concave down through (0, 0) to (0.5, negative 6) into the fourth quadrant. All values are estimated.

C)

A curve is graphed on an x y coordinate plane. The x axis ranges from negative 2 to 4, in increments of 0.5. The y axis ranges from negative 6 to 6, in increments of 1. The curve increases concave down through (negative 0.5, negative 5) and (0, 0) to (0.5, 2) and decreases concave up to (1.5, 0). It then increases concave up through (2, 2) to (2.5, 5) into the first quadrant. All values are estimated.

D)

A curve is graphed on an x y coordinate plane. The x axis ranges from negative 2 to 4, in increments of 0.5. The y axis ranges from negative 6 to 6, in increments of 1. The curve decreases concave up through (negative 0.5, 4) and (0, 0) to (0.5, negative 2) and increases concave down to (1.5, 0). It then decreases concave down to (2.5, negative 6) into the fourth quadrant. All values are estimated.

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 02

Learning Objective: Graph polynomial functions: x-intercepts; multiplicity (touch/cross) of each zero; end behavior.

22) Match the graph to the polynomial function.

A curve is graphed on an x y coordinate plane. The x axis ranges from negative 2 to 5, in increments of 0.5. The y axis ranges from negative 10 to 10, in increments of 2. The curve decreases concave up through (0, 8) to (1.5, 0) and moves along the horizontal axis from (1.5, 0) to (2.5, 0). It then decreases concave down to (4, negative 7.5) into the fourth quadrant. All values are estimated.

A) f of x equals negative left parenthesis x minus 2 right parenthesis cubed.

B) f of x equals left parenthesis x plus 2 right parenthesis cubed.

C) f of x equals negative left parenthesis x plus 2 right parenthesis cubed.

D) f of x equals left parenthesis x minus 2 right parenthesis cubed.

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 02

Learning Objective: Graph polynomial functions: x-intercepts; multiplicity (touch/cross) of each zero; end behavior.

23) For the polynomial function, (a) list each real zero and its multiplicity; (b) determine whether the graph touches or crosses at each x-intercept; (c) find the y-intercept; (d) determine the end behavior; and (e) sketch the graph.

f of x equals negative x left parenthesis 2 times x minus 3 right parenthesis squared.

Four options read as follows: a: 0, 1.5 (multiplicity 2); b: crosses at (0, 0), touches at (1.5, 0); c: (0, 0); d: behaves like y equals negative x cubed.

(e)

A curve is graphed on an x y coordinate plane. The x axis ranges from negative 2 to 4, in increments of 0.5. The y axis ranges from negative 6 to 6, in increments of 1. The curve decreases concave up through (negative 0.5, 4) and (0, 0) to (0.5, negative 2) and increases concave down to (1.5, 0). It then decreases concave down to (2.5, negative 6) into the fourth quadrant. All values are estimated.

Diff: 3 Var: 1

Chapter/Section: Ch 04, Sec 02

Learning Objective: Graph polynomial functions using transformations.

24) For the polynomial function, (a) list each real zero and its multiplicity; (b) determine whether the graph touches or crosses at each x-intercept; (c) find the y-intercept; (d) determine the end behavior; and (e) sketch the graph.

f of x equals negative x left parenthesis x minus 2 right parenthesis squared left parenthesis x minus 1 right parenthesis squared.

Four options read as follows: a: 0, 1 (multiplicity 2), 2 (multiplicity 2); b: crosses at (0, 0), touches at (1, 0) and (2, 0); c: (0, 0); d: behaves like y equals negative x to the power of 5.

(e)

A curve is graphed on an x y coordinate plane. The x axis ranges from negative 1 to 3, in increments of 1. The y axis has a marking at negative 1. The curve decreases concave up through (negative 0.1, 0.9) and (0, 0) to (0.2, negative 0.4). It then increases concave up to (1, 0), decreases concave up to (1.5, negative 0.2), increases concave up to (2, 0) and decreases concave down to (2.5, negative 1) into the fourth quadrant. All values are estimated.

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 02

Learning Objective: Graph polynomial functions using transformations.

25) For the given graph: (a) list each real zero and its smallest possible multiplicity; (b) determine whether the degree of the polynomial is even or odd; (c) determine whether the leading coefficient of the polynomial is positive or negative; (d) find the y-intercept; (e) write an equation for the polynomial function (assume the least degree possible).

A curve is graphed on an x y coordinate plane. The x axis ranges from negative 1 to 3, in increments of 1. The y axis has a marking at negative 1. The curve decreases concave up through (negative 0.1, 0.9) and (0, 0) to (0.2, negative 0.4). It then increases concave up to (1, 0), decreases concave up to (1.5, negative 0.2), increases concave up to (2, 0) and decreases concave down to (2.5, negative 1) into the fourth quadrant. All values are estimated.

Five options read as follows: a: 0, 1 (multiplicity 2), 2 (multiplicity 2); b: odd; c: negative; d: (0, 0); e: f of x equals negative x left parenthesis x minus 2 right parenthesis squared left parenthesis x minus 1 right parenthesis squared.

Diff: 3 Var: 1

Chapter/Section: Ch 04, Sec 02

Learning Objective: Graph polynomial functions: x-intercepts; multiplicity (touch/cross) of each zero; end behavior.

26) Graph the function by transforming a power function y = xn.

f (x) = 2(x) with superscript (6) + 3

A curve is graphed on a coordinate plane. The curve decreases concave up from the second quadrant to the positive vertical axis and then increases concave up through the first quadrant.

Diff: 3 Var: 1

Chapter/Section: Ch 04, Sec 02

Learning Objective: Graph polynomial functions using transformations.

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Chapter Number:
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Created Date:
Aug 21, 2025
Chapter Name:
Chapter 4 Polynomial And Rational Functions
Author:
Cynthia Y. Young

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