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Test Bank Docx Ch.2 Graphs

College Algebra, 5e (Young)

Chapter 2 Graphs

2.2 Graphing Equations: Point-Plotting, Intercepts, and Symmetry

1) Determine which point lies on the graph of the equation y = -10(x) with superscript (2) - 4x + 8.

A) (-222, 5)

B) (-222, -222)

C) (-262, 5)

D) (5, -262)

Diff: 1 Var: 1

Chapter/Section: Ch 02, Sec 02

Learning Objective: Sketch graphs of equations by plotting points.

2) Determine which point lies on the graph of the equation y = |7 - x| + 7.

A) (17, 3)

B) (3, 17)

C) (3, 11)

D) (0, 0)

Diff: 1 Var: 1

Chapter/Section: Ch 02, Sec 02

Learning Objective: Sketch graphs of equations by plotting points.

3) Which of the following applies to the graph y = (1/(x) with superscript (2))?

A) symmetry with respect to the x-axis

B) symmetry with respect to the y-axis

C) symmetry with respect to the origin

D) no symmetry

Diff: 1 Var: 1

Chapter/Section: Ch 02, Sec 02

Learning Objective: Conduct a test for symmetry about the x-axis, y-axis, and origin.

4) Which of the following applies to the graph 49(x) with superscript (2) + (y) with superscript (2) = 25?

A) symmetry with respect to the x-axis

B) symmetry with respect to the y-axis

C) symmetry with respect to the origin

D) no symmetry

Diff: 1 Var: 1

Chapter/Section: Ch 02, Sec 02

Learning Objective: Conduct a test for symmetry about the x-axis, y-axis, and origin.

5) Which of the following applies to the graph y = 5(x) with superscript (11)?

A) symmetry with respect to the x-axis

B) symmetry with respect to the y-axis

C) symmetry with respect to the origin

D) no symmetry

Diff: 1 Var: 1

Chapter/Section: Ch 02, Sec 02

Learning Objective: Conduct a test for symmetry about the x-axis, y-axis, and origin.

6) The point (-17, 18) lies on the graph that is symmetric about the x-axis. State the other point that must also lie on the graph.

A) (17, 18)

B) (17, -18)

C) (-17, -18)

D) (18, -17)

Diff: 1 Var: 1

Chapter/Section: Ch 02, Sec 02

Learning Objective: Conduct a test for symmetry about the x-axis, y-axis, and origin.

7) The point (1, -8) lies on the graph that is symmetric about the x-axis. State the other point that must also lie on the graph.

A) (1, 8)

B) (-1, -8)

C) (-1, 8)

D) (-8, 1)

Diff: 1 Var: 1

Chapter/Section: Ch 02, Sec 02

Learning Objective: Conduct a test for symmetry about the x-axis, y-axis, and origin.

8) The point (7, -5) lies on the graph that is symmetric about the y-axis. State the other point that must also lie on the graph.

A) (-5, 7)

B) (7, 5)

C) (-7, -5)

D) (-7, 5)

Diff: 1 Var: 1

Chapter/Section: Ch 02, Sec 02

Learning Objective: Conduct a test for symmetry about the x-axis, y-axis, and origin.

9) The point (-2, -10) lies on the graph that is symmetric about the y-axis. State the other point that must also lie on the graph.

A) (-10, -2)

B) (2, -10)

C) (-2, 10)

D) (2, 10)

Diff: 1 Var: 1

Chapter/Section: Ch 02, Sec 02

Learning Objective: Conduct a test for symmetry about the x-axis, y-axis, and origin.

10) The point (-10, 2) lies on the graph that is symmetric about the origin. State the other point that must also lie on the graph.

A) (2, -10)

B) (10, 2)

C) (-10, -2)

D) (10, -2)

Diff: 1 Var: 1

Chapter/Section: Ch 02, Sec 02

Learning Objective: Conduct a test for symmetry about the x-axis, y-axis, and origin.

11) The point (-7, -3) lies on the graph that is symmetric about the origin. State the other point that must also lie on the graph.

A) (-3, -7)

B) (7, 3)

C) (7, -3)

D) (-7, 3)

Diff: 1 Var: 1

Chapter/Section: Ch 02, Sec 02

Learning Objective: Conduct a test for symmetry about the x-axis, y-axis, and origin.

12) Use algebraic tests to determine whether the graph of the equation y = 10(x) with superscript (16) + 5(x) with superscript (9) is symmetric with respect to the x-axis, y-axis, or origin.

A) x-axis

B) y-axis

C) origin

D) no symmetry

Diff: 2 Var: 1

Chapter/Section: Ch 02, Sec 02

Learning Objective: Conduct a test for symmetry about the x-axis, y-axis, and origin.

13) Use algebraic tests to determine whether the graph of the equation 10(x) with superscript (2)+ 7(y) with superscript (2) = 9 is symmetric with respect to the x-axis, y-axis, or origin.

A) x-axis

B) y-axis

C) origin

D) x-axis, y-axis, origin

Diff: 2 Var: 1

Chapter/Section: Ch 02, Sec 02

Learning Objective: Conduct a test for symmetry about the x-axis, y-axis, and origin.

14) Use algebraic tests to determine whether the graph of the equation x = y + 18 is symmetric with respect to the x-axis, y-axis, or origin.

A) y-axis

B) x-axis

C) origin

D) no symmetry

Diff: 2 Var: 1

Chapter/Section: Ch 02, Sec 02

Learning Objective: Conduct a test for symmetry about the x-axis, y-axis, and origin.

15) The given point (-2, 3) lies on the graph that is symmetric about the x-axis, y-axis, and origin. State the other points that must also lie on the graph.

Diff: 2 Var: 1

Chapter/Section: Ch 02, Sec 02

Learning Objective: Conduct a test for symmetry about the x-axis, y-axis, and origin.

16) Use algebraic tests to determine whether the graph 5(x) with superscript (2) + 4(y) with superscript (2) = 1 is symmetric with respect to the x-axis, y-axis, or origin.

Diff: 1 Var: 1

Chapter/Section: Ch 02, Sec 02

Learning Objective: Conduct a test for symmetry about the x-axis, y-axis, and origin.

17) Use algebraic tests to determine whether the graph of y = 8(x) with superscript (3) - 6x is symmetric with respect to the x-axis, y-axis, or origin.

Diff: 1 Var: 1

Chapter/Section: Ch 02, Sec 02

Learning Objective: Conduct a test for symmetry about the x-axis, y-axis, and origin.

18) Plot the graph of the given equation.

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

A)

A parabola is 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 parabola opens rightward, with its vertex at (negative 1, 0). The parabola passes through the points (3, 2), (0, 1), (0, negative 1), and (3, negative 2). All values are estimated.

B)

A parabola 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 5 to 5, in increments of 0.5. The parabola opens downward, with its vertex at (0, 1). The parabola passes through the points (negative 2, negative 3), (negative 1, 0), (1, 0), and (2, negative 3). All values are estimated.

C)

A parabola 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 4 to 4, in increments of 0.5. The parabola opens leftward, with its vertex at (1, 0). The parabola passes through the points (negative 3, negative 2), (0, negative 1), (0, 1), and (negative 3, 2). All values are estimated.

D)

A parabola is 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 5 to 5, in increments of 0.5. The parabola opens upward, with its vertex at (0, negative 1). The parabola passes through the points (negative 2, 3), (negative 1, 0), (1, 0), and (2, 3). All values are estimated.

Diff: 2 Var: 1

Chapter/Section: Ch 02, Sec 02

Learning Objective: Use intercepts and symmetry as graphing aids.

19) The profit associated with making a particular product is given by the equation

y = -(x) with superscript (2) + 10x - 21

where y represents the profit in millions of dollars and x represents the number of thousands of units sold. (x = 1 corresponds to 1000 units and y = 1 corresponds to $1M.) Graph this equation and determine how many units must be sold to break even (profit = 0). Determine the range of units sold that correspond to making a profit.

A)

A downward opening parabola is graphed in an x y coordinate plane. The x axis ranges from negative 2 to 10 in increments of 2 and the y axis ranges from negative 20 to 4 in increments of 4. The parabola increases through (0, negative 20), and (3, 0) to vertex at (5, 4). It then decreases through (7, 0).

3000 units or 7000 units must be sold to break even

range of units sold that correspond to making a profit is 3000 to 7000

B)

An upward opening parabola is graphed in an x y coordinate plane. The x axis ranges from negative 2 to 10 in increments of 2 and the y axis ranges from negative 4 to 24 in increments of 4. The parabola decreases through (0, 22), and (3, 0) to vertex at (5, negative 4). It then increases through (7, 0).

3000 units or 7000 units must be sold to break even

range of units sold that correspond to making a profit is 3000 to 7000

C)

A downward opening parabola is graphed in an x y coordinate plane. The x axis ranges from negative 2 to 10 in increments of 2 and the y axis ranges from negative 20 to 4 in increments of 4. The parabola increases through (0, negative 20), and (3, 0) to vertex at (5, 4). It then decreases through (7, 0).

3000 units or 7000 units must be sold to break even

range of units sold that correspond to making a profit is from 0 to 3000 or at least 7000

D)

An upward opening parabola is graphed in an x y coordinate plane. The x axis ranges from negative 2 to 10 in increments of 2 and the y axis ranges from negative 4 to 24 in increments of 4. The parabola decreases through (0, 22), and (3, 0) to vertex at (5, negative 4). It then increases through (7, 0).

3000 units or 7000 units must be sold to break even

range of units sold that correspond to making a profit is from 0 to 3000 or at least 7000

Diff: 2 Var: 1

Chapter/Section: Ch 02, Sec 02

Learning Objective: Use intercepts and symmetry as graphing aids.

20) Use symmetry to help you graph the equation.

An equation reads, y squared minus x squared equals 9.

A longitudinal axis hyperbola is graphed in an x y coordinate plane. The x and y axes range from negative 6 to 6 in increments of 2. The upper branch runs through (negative 4, 4.5), (0, 3), and (4, 4.5). The right branch runs through (negative 4, negative 4.5), (0, negative 3), and (4, negative 4.5).

Diff: 2 Var: 1

Chapter/Section: Ch 02, Sec 02

Learning Objective: Use intercepts and symmetry as graphing aids.

21) Use symmetry to help you graph the equation.

An equation reads, x squared plus start fraction y squared over 25 end fraction equals 1.

A)

A vertical major axis ellipse is graphed in an x y coordinate plane. The x and y axes range from negative 6 to 6 in increments of 2. The ellipse is centered at the origin and it passes through the following points: (1, 0), (0, negative 5), (negative 1, 0), and (0, 5).

B)

A horizontal major axis ellipse is graphed in an x y coordinate plane. The x and y axes range from negative 6 to 6 in increments of 2. The ellipse is centered at the origin and it passes through the following points: (5, 0), (0, negative 1), (negative 5, 0), and (0, 1).

C)

A transverse axis hyperbola is graphed in an x y coordinate plane. The x and y axes range from negative 6 to 6 in increments of 2. The left branch decreases through (negative 4, 4), (negative 3, 0), and (negative 4, negative 4). The right branch decreases through (4, 4), (3, 0), and (4, negative 4).

D)

A transverse axis hyperbola is graphed in an x y coordinate plane. The x axis ranges from negative 8 to 8 in increments of 4 and the y axis ranges from negative 4 to 4 in increments of 2. The left branch decreases through (negative 8, 4), (negative 5, 0), and (negative 8, negative 4). The right branch decreases through (8, 4), (5, 0), and (8, negative 4).

Diff: 2 Var: 1

Chapter/Section: Ch 02, Sec 02

Learning Objective: Use intercepts and symmetry as graphing aids.

22) Use symmetry to help you graph the equation.

An equation reads, x squared plus y equals 16.

A)

A parabola 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 4 to 18, in increments of 2. The parabola opens downward, with its vertex at (0, 16). The parabola passes through the points (negative 4, 0) and (4, 0). All values are estimated.

B)

A transverse axis hyperbola is graphed in an x y coordinate plane. The x axis ranges from negative 8 to 8 in increments of 4 and the y axis ranges from negative 8 to 8 in increments of 2. The left branch decreases through (negative 8, 6), (negative 5, 0), and (negative 8, negative 6). The right branch decreases through (8, 6), (5, 0), and (8, negative 6).

C)

Two curves are graphed on an x y coordinate plane. Both the axes range from negative 8 to 8 in increments of 1. The first curve opens upward and passes through the points (negative 7, 8), (0, 4), and (7, 8). The second curve opens downward and passes through the points (negative 7, negative 8), (0, negative 4), and (7, negative 8). All values are estimated.

D)

A circle of radius 4 units is graphed on an x y coordinate plane. Both the axes range from negative 5 to 5 in increments of 0.5. The circle is centered at the origin and passes through the points (negative 4, 0), (0, 4), (4, 0), and (0, negative 4).

Diff: 2 Var: 1

Chapter/Section: Ch 02, Sec 02

Learning Objective: Use intercepts and symmetry as graphing aids.

23) Use symmetry to help you graph the equation.

An equation reads, x equals y squared plus 5.

A)

A rightward opening parabola is graphed in an x y coordinate plane. The x axis ranges from negative 2 to 14 in increments of 2 and the y axis ranges from negative 4 to 4 in increments of 1. The parabola decreases through (12, 2.5) to vertex at (negative 5, 0). It then decreases through (12, negative 2.5).

B)

An upward opening parabola is graphed in an x y coordinate plane. The x axis ranges from negative 4 to 4 in increments of 1 and the y axis ranges from negative 6 to 6 in increments of 2. The parabola decreases through (negative 2.25, 0) to vertex at (0, negative 5). It then increases through (2.25, 0).

C)

An upward opening parabola is graphed in an x y coordinate plane. The x axis ranges from negative 4 to 4 in increments of 1 and the y axis ranges from negative 2 to 12 in increments of 2. The parabola decreases through (negative 3, 12) to vertex at (0, 5). It then increases through (3, 12).

D)

A rightward opening parabola is graphed in an x y coordinate plane. The x axis ranges from negative 3 to 6 in increments of 1 and the y axis ranges from negative 4 to 4 in increments of 1. The parabola decreases through (0, 2.25) to vertex at (negative 5, 0). It then decreases through (0, negative 2.25).

Diff: 2 Var: 1

Chapter/Section: Ch 02, Sec 02

Learning Objective: Use intercepts and symmetry as graphing aids.

24) Match the graph with the corresponding symmetry.

A longitudinal axis hyperbola is graphed in an x y coordinate plane. The x axis ranges from negative 6 to 6 in increments of 2 and the y axis ranges from negative 6 to 6 in increments of 2. The upper branch runs through (negative 6, 6), (0, 2), and (6, 6). The lower branch runs through (negative 6, negative 6), (0, negative 2), and (6, negative 6).

A) Symmetry with respect to the x-axis

B) No symmetry

C) Symmetry with respect to the y-axis

D) Symmetry with respect to the x-axis, y-axis, and origin

E) Symmetry with respect to the origin

Diff: 2 Var: 1

Chapter/Section: Ch 02, Sec 02

Learning Objective: Use intercepts and symmetry as graphing aids.

25) Complete the table for the given equation.

x

y = 5x - 4

(x, y)

-6

-4

-2

0

x

y = 5x - 4

(x, y)

-6

-34

(-6, -34)

-4

-24

(-4, -24)

-2

-14

(-2, -14)

0

-4

(0, -4)

Diff: 1 Var: 1

Chapter/Section: Ch 02, Sec 02

Learning Objective: Sketch graphs of equations by plotting points.

26) Complete the table for the given equation.

x

y = square root of (x + 4)

(x, y)

-3

0

5

12

x

y = square root of (x + 4)

(x, y)

-3

1

(-3, 1)

0

2

(0, 2)

5

3

(5, 3)

12

4

(12, 4)

Diff: 1 Var: 1

Chapter/Section: Ch 02, Sec 02

Learning Objective: Sketch graphs of equations by plotting points.

27) Find the x-intercept(s).

3x + 2y = 6

(2, 0)

Diff: 1 Var: 1

Chapter/Section: Ch 02, Sec 02

Learning Objective: Find intercepts for graphs of equations.

28) Find the y-intercept(s).

-5x + 3y = 9

(3, 0)

Diff: 1 Var: 1

Chapter/Section: Ch 02, Sec 02

Learning Objective: Find intercepts for graphs of equations.

29) Find the x-intercept(s).

y = (x) with superscript (2) - 7x + 10

(2, 0) and (5, 0)

Diff: 1 Var: 1

Chapter/Section: Ch 02, Sec 02

Learning Objective: Find intercepts for graphs of equations.

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Document Information

Document Type:
DOCX
Chapter Number:
2
Created Date:
Aug 21, 2025
Chapter Name:
Chapter 2 Graphs
Author:
Cynthia Y. Young

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