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

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Test Bank Answers Ch4 Polynomial And Rational Functions

College Algebra, 5e (Young)

Chapter 4 Polynomial and Rational Functions

4.6 Rational Functions

1) Find the domain of the rational function f (x) = (25/12 - 6x).

A) (-∞, -2) ∪ (-2, ∞)

B) [25, ∞)

C) (-∞, 2] ∪ [2, ∞)

D) (-∞, 2) ∪ (2, ∞)

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 06

Learning Objective: Find the domain of a rational function.

2) Find the domain of the rational function.

f (x) = (5x + 3/(4x - 5)(x + 8))

A) (-∞, -8) ∪ (8, ∞)

B) (-∞, -8) ∪ (-8, 5/4) ∪ (5/4, ∞)

C) (-8, 5/4)

D) (-∞, -3/5) ∪ (3/5, ∞)

Diff: 3 Var: 1

Chapter/Section: Ch 04, Sec 06

Learning Objective: Find the domain of a rational function.

3) Find the domain of the rational function f (x) = (7x + 5/x(9x - 1)).

A) (-∞, 1/9) ∪ (1/9, ∞)

B) (-∞, 0) ∪ (0, 1/9) ∪ (1/9, ∞)

C) (1/9, ∞)

D) (-∞, -5/7) ∪ (-5/7, ∞)

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 06

Learning Objective: Find the domain of a rational function.

4) Find the domain of the function f (x) = (-14x + 4/(x) with superscript (2) + 54x + 15).

A) (-∞, 6) ∪ (9, ∞)

B) (-∞, -9) ∪ (-9, -6) ∪ (-6, ∞)

C) (-∞, 6) ∪ (6, 9) ∪ (6, ∞)

D) (-∞, 6] ∪ [6, 9] ∪ [6, ∞)

Diff: 3 Var: 1

Chapter/Section: Ch 04, Sec 06

Learning Objective: Find the domain of a rational function.

5) Find the domain of the function f (x) = (-15x/(x) with superscript (2) + 25).

A) (-5, 5)

B) (-∞, -5) ∪ (-5, 5) ∪ (5, ∞)

C) (-∞, -5) ∪ (5, ∞)

D) (-∞, ∞)

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 06

Learning Objective: Find the domain of a rational function.

6) For the rational function f (x) = (7x + 14/4x + 19), find all the vertical asymptotes and horizontal asymptotes.

A) vertical asymptote is x = - (19/4), horizontal is y = (7/4)

B) vertical asymptote is x = (7/4), horizontal is y = - (19/4)

C) vertical asymptote is x = (14/19), horizontal is y = (7/4)

D) vertical asymptote is x = (19/4), horizontal is y = (14/19)

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 06

Learning Objective: Determine vertical, horizontal, and slant asymptotes of rational functions.

7) For the rational function f (x) = (2(x) with superscript (2) + 8x + 16/(x) with superscript (2) + 8x + 7), find all vertical and horizontal asymptotes.

A) vertical asymptotes x = -1 and x = -7, horizontal asymptote y = 2

B) vertical asymptotes x = -1 and x = -7, horizontal asymptote y = (1/2)

C) no vertical asymptotes, horizontal asymptote y = 2

D) vertical asymptotes x = 1 and x = 7, horizontal asymptote y = (1/2)

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 06

Learning Objective: Determine vertical, horizontal, and slant asymptotes of rational functions.

8) For the rational function f (x) = (125 - (x) with superscript (3)/(x) with superscript (2) + 10x + 25), find all vertical and horizontal asymptotes.

A) vertical asymptote at 5, there is no horizontal asymptote

B) vertical asymptote at -5, horizontal asymptote at 5

C) vertical asymptote at -5, there is no horizontal asymptote

D) vertical asymptote at 5, horizontal asymptote at -5

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 06

Learning Objective: Determine vertical, horizontal, and slant asymptotes of rational functions.

9) Professor Ito is teaching a large lecture course and is trying to learn students' names. The number of names he can remember, N(t), increases with each week in the semester, t, and is given by the rational function:

N(t) = (500t/t + 20)

How many students' names does Professor Ito know by the fourth week of the semester? How many students' names should he know by the end of the semester (16 weeks)? Round your answer to the nearest whole number.

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 06

Learning Objective: Graph rational functions.

10) Use the graphing strategy to graph the rational function.

f of x equals start fraction 2 times x over x squared minus 3 end fraction.

A function of two curves and two dashed lines are graphed on an x y coordinate plane. The x axis ranges from negative 4 to 8, in increments of 1. The y axis ranges from negative 8 to 8, in increments of 1. The first line is a vertical line that passes through (3, 0). The second line is a horizontal line that passes through (0, 2). The first curve decreases concave down from close to and below the second line in the second quadrant toward the left of the first line into the fourth quadrant with its vertex at (2, negative 2). The second curve decreases concave up from close to and above the second line in the first quadrant toward the right of the first line into the first quadrant with its vertex at (4, 6). All values are estimated.

Diff: 3 Var: 1

Chapter/Section: Ch 04, Sec 06

Learning Objective: Graph rational functions.

11) Match the rational function to the graph.

f of x equals start fraction 4 times x squared over x squared plus 1 end fraction.

A)

A function of a curve and a dashed line is graphed on an x y coordinate plane. The x axis ranges from negative 4 to 4, in increments of 0.5. The y axis ranges from negative 1 to 5, in increments of 0.5. The line is a horizontal line that passes through (0, 4). The curve decreases concave down from close to and below the line in the second quadrant from (negative 4, 3.8) to (0, 0). It then increases concave up to (4, 3.8). All values are estimated.

B)

A function of three curves and three dashed lines are graphed on an x y coordinate plane. The x axis ranges from negative 3 to 3, in increments of 0.5. The y axis ranges from negative 6 to 8, in increments of 1. The first line is a vertical line that passes through (negative 1, 0). The second line is a vertical line that passes through (1, 0). The third line is a horizontal line that passes through (0, 4). The first curve increases concave up from close to and above the third line in the second quadrant toward the left of the first line with its vertex at (negative 2, 5). The second curve is inverted U-shaped and extends in between both the vertical dashed lines through (negative 0.6, negative 6), (0, 0), and (0.6, negative 6). The third curve decreases concave up from close to and above the third line in the first quadrant toward the right of the second line with its vertex at (1.5, 6). All values are estimated.

C)

A function of a curve and a dashed line is graphed on an x y coordinate plane. The x axis ranges from negative 3 to 3, in increments of 0.5. The y axis ranges from negative 1.0 to 2.0, in increments of 0.25. The line is a horizontal line that passes through (0, 1.0). The curve decreases concave down from close to and below the line in the second quadrant from (negative 3, 0.75) to (0, 0). It then increases concave up to (3, 0.75). All values are estimated.

D)

A function of three curves and three dashed lines are graphed on an x y coordinate plane. The x axis ranges from negative 5 to 5, in increments of 0.5. The y axis ranges from negative 4 to 4, in increments of 0.5. The first line is a vertical line that passes through (negative 2, 0). The second line is a vertical line that passes through (2, 0). The third line is a horizontal line that passes through (0, 1). The first curve increases concave up from close to and above the third line in the second quadrant toward the left of the first line with its vertex at (negative 3, 2). The second curve is inverted U-shaped and extends in between both the vertical dashed lines through (negative 1.8, negative 4), (0, 0) and (1.8, negative 4). The third curve decreases concave up from close to and above the third line in the first quadrant toward the right of the second line with its vertex at (2.5, 2). All values are estimated.

Diff: 3 Var: 1

Chapter/Section: Ch 04, Sec 06

Learning Objective: Graph rational functions.

12) Match the graph to the rational function.

A function of two curves and two dashed lines are graphed on an x y coordinate plane. The x axis ranges from negative 8 to 4, in increments of 1. The y axis ranges from negative 8 to 8, in increments of 1. The first line is a vertical line that passes through (negative 3, 0). The second line is a horizontal line that passes through (0, 2). The first curve increases concave up from close to and above the second line in the second quadrant toward the left of the first line in the second quadrant with its vertex at (negative 5, 5). The second curve increases concave down from below the second line in the third quadrant close to and toward the right of the first line into the first quadrant with its vertex at (negative 2, negative 2). All values are estimated.

A) f of x equals start fraction 2 times x over x plus 3 end fraction.

B) f of x equals start fraction 2 times x over x minus 3 end fraction.

C) f of x equals start fraction 3 times x over x plus 2 end fraction.

D) f of x equals start fraction 3 times x over x minus 2 end fraction.

Diff: 4 Var: 1

Chapter/Section: Ch 04, Sec 06

Learning Objective: Graph rational functions.

13) For the given graph of the rational function determine: (a) all intercepts, (b) all asymptotes, and (c) equation of the rational function.

A function of two curves and two dashed lines are graphed on an x y coordinate plane. The x axis ranges from negative 4 to 8, in increments of 1. The y axis ranges from negative 8 to 8, in increments of 1. The first line is a vertical line that passes through (3, 0). The second line is a horizontal line that passes through (0, 2). The first curve decreases concave down from close to and below the second line in the second quadrant toward the left of the first line into the fourth quadrant with its vertex at (2, negative 2). The second curve decreases concave up from close to and above the second line in the first quadrant toward the right of the first line into the first quadrant with its vertex at (4, 6). All values are estimated.

Three options read as follows: a: x-intercept: (0, 0); y-intercept: (0, 0); b: H A: y equals 2; V A: x equals 3; c: f of x equals start fraction 2 times x over x minus 3 end fraction.

Diff: 3 Var: 1

Chapter/Section: Ch 04, Sec 06

Learning Objective: Graph rational functions.

14) For the given graph of the rational function determine: (a) all intercepts, (b) all asymptotes, and (c) equation of the rational function.

A function of three curves and three dashed lines are graphed on an x y coordinate plane. The x axis ranges from negative 5 to 5, in increments of 0.5. The y axis ranges from negative 8 to 8, in increments of 1. The first line is a vertical line that passes through (negative 2, 0). The second line is a vertical line that passes through (2, 0). The third line is an upward sloping line that passes through (0, 0). The first curve increases concave down from close to and below the third line in the second quadrant toward the left of the first line in the third quadrant with its vertex at (negative 2.5, negative 5). The second curve extends in between both the vertical dashed lines through (negative 1.9, 7), (negative 1, 0), (1, 0) and (1.9, negative 7). The third curve decreases concave up from close to and above the third line in the first quadrant toward the right of the second line with its vertex at (2.5, 5). All values are estimated.

A)

Three options read as follows: a: x-intercept: (negative 2, 0), (0, 0),(2, 0); y-intercept: (0, 0); b: S A: y equals x; V A: x equals negative 1, x equals 1; c: f of x equals start fraction x left parenthesis x squared minus 4 right parenthesis over left parenthesis x squared minus 1 right parenthesis end fraction.

B)

Three options read as follows: a: x-intercept: (negative 2, 0), (0, 0), (1, 0); y-intercept: (0, 0); b: S A: y equals x plus 2; V A: x equals negative 1, x equals 2; c: f of x equals start fraction x left parenthesis x plus 2 right parenthesis left parenthesis x minus 1 right parenthesis over left parenthesis x minus 2 right parenthesis left parenthesis x plus 1 right parenthesis end fraction.

C)

Three options read as follows: a: x-intercept: (negative 1, 0), (0, 0), (1, 0); y-intercept: (0, 0); b: S A: y equals x; V A: x equals negative 2, x equals 2; c: f of x equals start fraction x left parenthesis x squared minus 1 right parenthesis over left parenthesis x squared minus 4 right parenthesis end fraction.

D)

Three options read as follows: a: x-intercept: (negative 1, 0), (1, 0),(2, 0); y-intercept: (0, 0); b: S A: y equals x minus 2; V A: x equals negative 2, x equals 1; c: f of x equals start fraction x left parenthesis x minus 2 right parenthesis left parenthesis x plus 1 right parenthesis over left parenthesis x plus 2 right parenthesis left parenthesis x minus 1 right parenthesis end fraction.

Diff: 3 Var: 1

Chapter/Section: Ch 04, Sec 06

Learning Objective: Graph rational functions.

15) For the rational function f (x) = (6(x) with superscript (3) + 2(x) with superscript (2) + 8x - 10/2(x) with superscript (2) + 2x + 3), find the equation of the slant asymptote.

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 06

Learning Objective: Determine vertical, horizontal, and slant asymptotes of rational functions.

16) For the rational function f (x) = (18(x) with superscript (2) - 21x + 11/6x - 3), find the equation of the slant asymptote.

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 06

Learning Objective: Determine vertical, horizontal, and slant asymptotes of rational functions.

17) Use the graphing strategy to graph the rational function.

f (x) = (x - 2/(x) with superscript (2) + 2x + 9)

A blank Cartesian grid. Both the axes range from negative 5 to 5, in increments of 1.

Diff: 3 Var: 1

Chapter/Section: Ch 04, Sec 06

Learning Objective: Graph rational functions.

18) Use the graphing strategy to graph the rational function.

f (x) = ((x) with superscript (2) + 6/(x) with superscript (4) - 12)

A blank Cartesian grid. Both the axes range from negative 5 to 5, in increments of 1.

Diff: 3 Var: 1

Chapter/Section: Ch 04, Sec 06

Learning Objective: Graph rational functions.

19) Use the graphing strategy to graph the rational function.

f (x) = ((x) with superscript (6) + 6/(x) with superscript (2) - 5)

A blank Cartesian grid. Both the axes range from negative 5 to 5, in increments of 1.

Diff: 3 Var: 1

Chapter/Section: Ch 04, Sec 06

Learning Objective: Graph rational functions.

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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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