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Functions And Their Graphs Chapter.3 Test Bank Answers 5e

College Algebra, 5e (Young)

Chapter 3 Functions and Their Graphs

3.3 Graphing Techniques: Transformations

1) The graph of y = |x| shifted down 5 and to the right 14. Write the resulting function.

A) y = |x + 14| - 5

B) y = |x - 14| - 5

C) y = |x + 14| + 5

D) y = |x - 14| + 5

Diff: 1 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function using horizontal and vertical shifting of common functions.

2) The graph of y = |x| shifted up 1 and to the left 20. Write the resulting function.

A) y = |x + 20| + 1

B) y = |x - 20| - 1

C) y = |x - 1| - 20

D) y = |x + 1| + 20

Diff: 1 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function using horizontal and vertical shifting of common functions.

3) The graph of y = (x) with superscript (2) is shifted up 8 and to the left 13. Write the resulting function.

A) y = ((x - 13)) with superscript (2) - 8

B) y = ((x - 8)) with superscript (2) - 13

C) y = ((x + 8)) with superscript (2) + 13

D) y = ((x + 13)) with superscript (2) + 8

Diff: 1 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function using horizontal and vertical shifting of common functions.

4) The graph of y = (x) with superscript (2) is reflected about the x-axis and shifted to the right 8. Write the resulting function.

A) y = -((x - 8)) with superscript (2)

B) y = -((x + 8)) with superscript (2)

C) y = ((x - 8)) with superscript (2)

D) y = ((-x - 8)) with superscript (2)

Diff: 1 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function using a sequence of transformations.

5) The graph of y = |x| is reflected about the x-axis and shifted up 5. Write the resulting function.

A) y = |x| + 5

B) y = - |x + 5|

C) y = - |x| + 5

D) y = - |x - 5|

Diff: 1 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function using a sequence of transformations.

6) The graph of y = (x) with superscript (3) is expanded by a factor of 5. Write the resulting function.

A) y = 5(x) with superscript (3)

B) y = (x) with superscript (3) - 5

C) y = (x) with superscript (3) + 5

D) y = (1/5)(x) with superscript (3)

Diff: 1 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function by stretching or compressing a common function.

7) The graph of y = (x) with superscript (3) is contracted by a factor of 7. Write the resulting function.

A) y = 7(x) with superscript (3)

B) y = (x) with superscript (3) - 7

C) y = (x) with superscript (3) + 7

D) y = (1/7)(x) with superscript (3)

Diff: 1 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function by stretching or compressing a common function.

8) The graph of y = (x) with superscript (4) is contracted by a factor of 7. Write the resulting function.

A) y = 7(x) with superscript (4)

B) y = (x) with superscript (4) - 7

C) y = (x) with superscript (4) + 7

D) y = (1/7)(x) with superscript (4)

Diff: 1 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function by stretching or compressing a common function.

9) The graph of y = (x) with superscript (4) is expanded by a factor of 3. Write the resulting function.

A) y = 3(x) with superscript (4)

B) y = (x) with superscript (4) - 3

C) y = (x) with superscript (4) + 3

D) y = (1/3)(x) with superscript (4)

Diff: 1 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function by stretching or compressing a common function.

10) The graph of y = square root of (x) is reflected about the x-axis and shifted to the left 5. Write the resulting function.

A) y = - square root of (x) + 5

B) y = square root of (-x + 5)

C) y = - square root of (x + 5)

D) y = - square root of (x - 5)

Diff: 2 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function using a sequence of transformations.

11) The graph of y = square root of (x) is reflected about the x-axis and shifted to the right 3 and up 7. Write the resulting function.

A) y = - square root of (x - 3) + 7

B) y = - square root of (x + 3) + 7

C) y = - square root of (x - 7) + 3

D) y = - square root of (x + 7) + 3

Diff: 2 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function using a sequence of transformations.

12) Write the function that results from shifting y = (x) with superscript (2) + 7 to the left 2 and reflecting about the x-axis.

A) y = -((x + 2)) with superscript (2) - 7

B) y = -((x - 2)) with superscript (2) - 7

C) y = -((x + 2)) with superscript (2) + 7

D) y = -((x - 2)) with superscript (2) + 7

Diff: 2 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function using a sequence of transformations.

13) Write the function that results from shifting y = square root of (x) to the right 8 and up 7.

A) y = square root of (x + 8) + 7

B) y = square root of (x - 8) + 7

C) y = square root of (x - 8) - 7

D) y = square root of (x - 7) + 8

Diff: 1 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function using horizontal and vertical shifting of common functions.

14) Write the function resulting from shifting f (x) = 2(x) with superscript (2) + 9 to the left 7 and up 8.

A) y = 2((x + 7)) with superscript (2) + 17

B) y = 2((x + 7)) with superscript (2) + 8

C) y = 2((x - 7)) with superscript (2) + 8

D) y = 2((x - 7)) with superscript (2) + 17

Diff: 2 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function using horizontal and vertical shifting of common functions.

15) The graph of y = (x) with superscript (2) is expanded by a factor of 2, shifted to the left 5, and up 14. Write the resulting function.

Diff: 2 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function using a sequence of transformations.

16) The graph of y = |x| + 1 is expanded by a factor of 6 and reflected about the x-axis. Write the resulting function.

Diff: 2 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function using a sequence of transformations.

17) Transform the function f (x) = 7(x) with superscript (2) + 14x + 0 to the form f (x) = c((x - h)) with superscript (2) + k, where c, h, and k are constants, by completing the square.

Diff: 2 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function using a sequence of transformations.

18) Transform the function f (x) = 8(x) with superscript (2) - 96x + 297 to the form f (x) = c((x - h)) with superscript (2) + k, where c, h, and k are constants, by completing the square.

Diff: 2 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function using a sequence of transformations.

19) Transform the function f (x) = -2(x) with superscript (2) - 12x - 18 to the form f (x) = c((x - h)) with superscript (2) + k, where c, h, and k are constants, by completing the square.

Diff: 2 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function using a sequence of transformations.

20) Transform the function f (x) = 7(x) with superscript (2) - 70x to the form f (x) = c((x - h)) with superscript (2) + k, where c, h, and k are constants, by completing the square.

Diff: 2 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function using a sequence of transformations.

21) For the given graph of a function f (x) draw the indicated function.

A line function is graphed on an x y coordinate plane. The x axis ranges from negative 8 to 8, in increments of 1. The y axis ranges from negative 5 to 8, in increments of 1. The line slopes downward to the right from (negative 4, 7) to (negative 2, negative 1), then moves horizontally to the right to (2, negative 1), and then slopes upward to the right to (4, 7). All values are estimated.

y = f (x - 3) - 2

A line is graphed in an x y plane, where the x axis ranges from negative 8 to 8 in increments of 2 and the y axis ranges from negative 4 to 6 in increments of 2. The line passes through the following points in the following order: (negative 1, 5), (0, 1), (1, negative 3), (5, negative 3), and (7, 5).

Diff: 2 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function using horizontal and vertical shifting of common functions.

22) For the given graph of a function f (x) draw the indicated function.

A line function is graphed on an x y coordinate plane. The x axis ranges from negative 6 to 6, in increments of 1. The y axis ranges from negative 6 to 8, in increments of 1. The line slopes downward to the right from (negative 4, 7) to (negative 2, negative 1), then moves horizontally to the right to (2, negative 1), and then slopes upward to the right to (4, 7). All values are estimated.

f (x + 2) - 3

A line function is graphed on an x y coordinate plane. The x axis ranges from negative 10 to 6, in increments of 1. The y axis ranges from negative 6 to 8, in increments of 1. The line slopes downward to the right from (negative 6, 4) to (negative 4, negative 4), then moves horizontally to the right to (0, negative 4), and then slopes upward to the right to (2, 4). All values are estimated.

Diff: 2 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function using horizontal and vertical shifting of common functions.

23) For the given graph of a function f (x) draw the indicated function.

A line function is graphed on an x y coordinate plane. The x axis ranges from negative 6 to 6, in increments of 1. The y axis ranges from negative 6 to 8, in increments of 1. The line slopes downward to the right from (negative 4, 7) to (negative 2, negative 1), then moves horizontally to the right to (2, negative 1), and then slopes upward to the right to (4, 7). All values are estimated.

-2f (x - 1) + 3

A line is graphed in an x y plane, where the x axis ranges from negative 6 to 6 in increments of 2 and the y axis ranges from negative 12 to 8 in increments of 4. The line passes through the following points in the following order: (negative 3, negative 11), (negative 1, 5), (3, 5), and (5, negative 11).

Diff: 2 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function using a sequence of transformations.

24) For the given graph of a function f (x) draw the indicated function.

A line function is graphed on an x y coordinate plane. The x axis ranges from negative 6 to 6, in increments of 1. The y axis ranges from negative 6 to 8, in increments of 1. The line slopes downward to the right from (negative 4, 7) to (negative 2, negative 1), then moves horizontally to the right to (2, negative 1), and then slopes upward to the right to (4, 7). All values are estimated.

-f (x) + 4

A line is graphed in an x y plane, where the x axis ranges from negative 6 to 6 in increments of 2 and the y axis ranges from negative 8 to 8 in increments of 2. The line passes through the following points in the following order: (negative 4, negative 3), (negative 2, 5), (2, 5), and (4, negative 3).

Diff: 2 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function by reflecting a common function about the x-axis or y-axis.

25) For the given graph of a function f (x) draw the indicated function.

A curve function is graphed on an x y coordinate plane. The x axis ranges from negative 5 to 5, in increments of 1. The y axis ranges from negative 4 to 4, in increments of 2. The curve is M-shaped. The curve increases from (negative 3, 0) to a maximum at (negative 2, 4), decreases to a minimum at (negative 1, 0), then increases to a maximum at (0, 4), and then decreases to a minimum at (1, 0). All values are estimated.

- (1/3) f (x)

A curve is graphed in an x y plane, where the x axis ranges from negative 5 to 5 in increments of 1 and the y axis ranges from negative 2 to 2 in increments of 2. The curve passes through the following points in the following order: (negative 3, 0), (negative 2, negative 1), (negative 1, 0), (0, negative 1), and (1, 0).

Diff: 2 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function using a sequence of transformations.

26) For the given graph of a function f (x) draw the indicated function.

A line function is graphed on an x y coordinate plane. The x axis ranges from negative 6 to 4, in increments of 2. The y axis ranges from negative 4 to 4, in increments of 2. The line slopes downward to the right from (negative 4, 1) to (negative 2, negative 1), then slopes upward to the right to (1, 2), and then slopes downward to the right to (4, negative 1). All values are estimated.

f ((1/2)x)

A line is graphed in an x y plane, where the x axis ranges from negative 8 to 8 in increments of 2 and the y axis ranges from negative 2 to 3 in increments of 1. The line passes through the following points in the following order: (negative 8, 1), (negative 4, negative 1), (2, 2), and (8, negative 1).

Diff: 2 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function by stretching or compressing a common function.

27) For the given graph of a function f (x) draw the indicated function.

A curve is graphed in an x y plane, where the x axis ranges from negative 5 to 5 in increments of 1 and the y axis ranges from negative 4 to 4 in increments of 2. The curve passes through the following points in the following order: (negative 3, 0), (negative 2, 4), (negative 1, 0), (0, 4), and (1, 0).

f (2x)

A curve is graphed in an x y plane, where the x axis ranges from negative 2 to 2 in increments of 1 and the y axis ranges from negative 2 to 4 in increments of 2. The curve passes through the following points in the following order: (negative 1.5, 0), (negative 1, negative 4), (negative 0.5, 0), (0, 4), and (0.5, 0).

Diff: 2 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function by stretching or compressing a common function.

28) For the given graph of a function f (x) draw the indicated function.

A line function is graphed on an x y coordinate plane. The x axis ranges from negative 6 to 6, in increments of 2. The y axis ranges from negative 4 to 4, in increments of 2. The line slopes downward to the right from (negative 4, 1) to (negative 2, negative 1), then slopes upward to the right to (1, 2), and then slopes downward to the right to (4, negative 1). All values are estimated.

f (x + 2) - 2

A line function is graphed on an x y coordinate plane. The x axis ranges from negative 6 to 6, in increments of 2. The y axis ranges from negative 4 to 4, in increments of 2. The line slopes downward to the right from (negative 6, negative 1) to (negative 4, negative 3), then slopes upward to the right to (negative 1, 0), and then slopes downward to the right to (2, negative 3). All values are estimated.

Diff: 2 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function using a sequence of transformations.

29) For the given graph of a function f (x) draw the indicated function.

A curve function is graphed on an x y coordinate plane. The x axis ranges from negative 5 to 5, in increments of 1. The y axis ranges from negative 4 to 4, in increments of 2. The curve is M-shaped. The curve increases from (negative 3, 0) to a maximum at (negative 2, 4), decreases to a minimum at (negative 1, 0), then increases to a maximum at (0, 4), and then decreases to a minimum at (1, 0). All values are estimated.

- (1/2) f (x)

A)

A curve function is graphed on an x y coordinate plane. The x axis ranges from negative 5 to 4, in increments of 1. The y axis ranges from negative 2 to 2, in increments of 2. The curve is W-shaped. The curve decreases from (negative 3, 0) to a minimum at (negative 2, negative 2), increases to a maximum at (negative 1, 0), then decreases to a minimum at (0, negative 2), and then increases to a maximum at (1, 0). All values are estimated.

B)

A curve function is graphed on an x y coordinate plane. The x axis ranges from negative 5 to 4, in increments of 1. The y axis ranges from negative 2 to 2, in increments of 2. The curve is M-shaped. The curve increases from (negative 3, 0) to a maximum at (negative 2, 2), decreases to a minimum at (negative 1, 0), then increases to a maximum at (0, 2), and then decreases to a minimum at (1, 0). All values are estimated.

C)

A curve function is graphed on an x y coordinate plane. The x axis ranges from negative 2 to 1, in increments of 1. The y axis ranges from negative 2 to 1. The curve is W-shaped. The curve decreases from (negative 1.5, 0) to a minimum at (negative 1, negative 4), increases to a maximum at (negative 0.5, 0), then decreases to a minimum at (0, negative 4), and then increases to a maximum at (0.5, 0). All values are estimated.

D)

A curve function is graphed on an x y coordinate plane. The x axis ranges from negative 2 to 2, in increments of 1. The y axis ranges from negative 2 to 4, in increments of 2. The curve is M-shaped. The curve increases from (negative 1.5, 0) to a maximum at (negative 1, 4), decreases to a minimum at (negative 0.5, 0), then increases to a maximum at (0, 4), and then decreases to a minimum at (0.5, 0). All values are estimated.

Diff: 2 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function by stretching or compressing a common function.

30) For the given graph of a function f (x) draw the indicated function.

A line function is graphed on an x y coordinate plane. The x axis ranges from negative 8 to 8, in increments of 1. The y axis ranges from negative 6 to 6, in increments of 1. The line slopes downward to the right from (negative 1, 3) to (1, negative 5), then moves horizontally to the right to (5, negative 5), and then slopes upward to the right to (7, 3). All values are estimated.

y = f (x - 2) - 3

A)

A line function is graphed on an x y coordinate plane. The x axis ranges from negative 8 to 8, in increments of 1. The y axis ranges from negative 7 to 4, in increments of 0.5. The line slopes downward to the right from (negative 2, 4) to (0, negative 4), then moves horizontally to the right to (4, negative 4), and then slopes upward to the right to (6, 4). All values are estimated.

B)

A line function is graphed on an x y coordinate plane. The x axis ranges from negative 8 to 8, in increments of 1. The y axis ranges from negative 5 to 8, in increments of 1. The line slopes downward to the right from (negative 1, 5) to (1, negative 3), then moves horizontally to the right to (5, negative 3), and then slopes upward to the right to (7, 5). All values are estimated.

C)

A line function is graphed on an x y coordinate plane. The x axis ranges from negative 10 to 6, in increments of 1. The y axis ranges from negative 6 to 8, in increments of 1. The line slopes downward to the right from (negative 6, 4) to (negative 4, negative 4), then moves horizontally to the right to (0, negative 4), and then slopes upward to the right to (2, 4). All values are estimated.

D)

A line function is graphed on an x y coordinate plane. The x axis ranges from negative 10 to 6, in increments of 1. The y axis ranges from negative 6 to 8, in increments of 1. The line slopes downward to the right from (negative 7, 5) to (negative 5, negative 3), then moves horizontally to the right to (negative 1, negative 3), and then slopes upward to the right to (1, 5). All values are estimated.

Diff: 2 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function using horizontal and vertical shifting of common functions.

31) For the given graph of a function f (x) draw the indicated function.

A line function is graphed on an x y coordinate plane. The x axis ranges from negative 8 to 8, in increments of 1. The y axis ranges from negative 5 to 8, in increments of 1. The line slopes downward to the right from (negative 4, 7) to (negative 2, negative 1), then moves horizontally to the right to (2, negative 1), and then slopes upward to the right to (4, 7). All values are estimated.

y = f (x + 1) - 4

A)

A line function is graphed on an x y coordinate plane. The x axis ranges from negative 8 to 8, in increments of 1. The y axis ranges from negative 7 to 4, in increments of 0.5. The line slopes downward to the right from (negative 3, 3) to (negative 1, negative 5), then moves horizontally to the right to (3, negative 5), and then slopes upward to the right to (5, 3). All values are estimated.

B)

A line function is graphed on an x y coordinate plane. The x axis ranges from negative 6 to 10, in increments of 1. The y axis ranges from negative 6 to 8, in increments of 1. The line slopes downward to the right from (0, 5) to (2, negative 3), then moves horizontally to the right to (6, negative 3), and then slopes upward to the right to (8, 5). All values are estimated.

C)

A line function is graphed on an x y coordinate plane. The x axis ranges from negative 10 to 6, in increments of 1. The y axis ranges from negative 7 to 8, in increments of 1. The line slopes downward to the right from (negative 5, 3) to (negative 3, negative 5), then moves horizontally to the right to (1, negative 5), and then slopes upward to the right to (3, 3). All values are estimated.

D)

A line function is graphed on an x y coordinate plane. The x axis ranges from negative 10 to 6, in increments of 1. The y axis ranges from negative 6 to 8, in increments of 1. The line slopes downward to the right from (negative 8, 6) to (negative 6, negative 2), then moves horizontally to the right to (negative 2, negative 2), and then slopes upward to the right to (0, 6). All values are estimated.

Diff: 2 Var: 1

Chapter/Section: Ch 03, Sec 03

Learning Objective: Sketch the graph of a function using horizontal and vertical shifting of common functions.

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Document Type:
DOCX
Chapter Number:
3
Created Date:
Aug 21, 2025
Chapter Name:
Chapter 3 Functions And Their Graphs
Author:
Cynthia Y. Young

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