Test Bank for College Algebra Essentials 5th Edition Blitzer UPDATED 2025

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Ch. 2 Functions and Graphs
2.1 Basics of Functions and Their Graphs
1 Find the Domain and Range of a Relation
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Give the domain and range of the relation.
1) {(1, -7), (7, 1), (3, -1), (3, 4)}
A) domain = {1, 3, 7}; range = {-7, -1, 1, 4} B) domain = {-7, -1, 1, 4}; range = {1, 3, 7}
C) domain = {1, 3, 7, 13}; range = {-7, -1, 1, 4} D) domain = {1, 3, 7, -3}; range = {-7, -1, 1, 4}

2) {(6, 6), (11, -5), (3, 4), (3, -3)}
A) domain = {6, 3, 11}; range = {6, 4, -5, -3} B) domain = {6, 3, 11, -3}; range = {6, 4, -5, -3}
C) domain = {6, 3, 11, 13}; range = {6, 4, -5, -3} D) domain = {6, 4, -5, -3}; range = {6, 3, 11}

3) {(-4, -5), (9, -1), (7, 3), (-3, -3)}
A) domain = {9, -3, -4, 7}; range = {-1, -3, -5, 3}
B) domain = {-1, -3, -5, 3}; range = {9, -3, -4, 7}
C) domain = {9, -3, -4, 7}; range = {-1, 5, -3, -5, 3}
D) domain = {9, -3, -4, 7}; range = {-1, -1, -3, -5, 3}

4) {(-5, 1), (-5, 3), (9, 9), (4, -4), (-1, -1)}
A) domain = {4, -5, -1, 9}; range = {-4, 3, -1, 9, 1}
B) domain = {4, -4, -5, -1, 9}; range = {-4, 3, -1, 9, 1}
C) domain = {4, 14, -5, -1, 9}; range = {-4, 3, -1, 9, 1}
D) domain = {-4, 3, -1, 9, 1}; range = {4, 4, -5, -1, 9}

5) {(41, -3), (5, -2), (5, 0), (9, 2), (21, 4)}
A) domain: {41, 9, 5, 21}; range: {-3, -2, 0, 2, 4} B) domain: {-3, -2, 2, 4}; range: {41, 9, 5, 21}
C) domain: {-3, -2, 0, 2, 4}; range: {41, 9, 5, 21} D) domain: {41, 9, 5, 21}; range: {-3, -2, 2, 4}

6) {(6, -5), (3, 2), (4, 6), (-1, 3), (-4, 9)}
A) domain = {4, -1, 3, 6, -4}; range = {6, 3, 2, -5, 9}
B) domain = {6, 3, 2, -5, 9}; range = {4, -1, 3, 6, -4}
C) domain = {4, 6, -1, 3, 3}; range = {2, 6, -5, -4, 9}
D) domain = {2, 6, -5, -4, 9}; range = {4, 6, -1, 3, 3}

7) {(-2, 6), (-1, 3), (0, 2), (1, 3), (3, 11)}
A) domain: {-2, -1, 0, 1, 3}; range: {6, 3, 2, 11} B) domain: {-2, -1, 1, 3}; range: {6, 3, 2, 11}
C) domain: {6, 3, 2, 11}; range: {-2, -1, 0, 1, 3} D) domain: {6, 3, 2, 11}; range: {-2, -1, 1, 3}

2 Determine Whether a Relation is a Function
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Determine whether the relation is a function.
1) {(-1, -6), (2, -5), (4, 9), (8, -5), (10, 3)}
A) Function B) Not a function

2) {(-6, 3), (-1, 3), (1, -1), (1, 1)}
A) Not a function B) Function




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3) {(-6, 8), (-6, -5), (2, -8), (6, -8), (9, 6)} 9) y = - x - 8
A) Not a function B) Function A) y is a function of x B) y is not a function of x

4) {(1, -2), (1, -4), (4, -3), (9, -1), (12, 5)} 10) y = 6x - 2
A) Not a function B) Function A) y is a function of x B) y is not a function of x

5) {(-5, 4), (-2, 9), (4, 8), (5, 2)}
11) x + y 3 = 1
A) Function B) Not a function
A) y is a function of x B) y is not a function of x
6) {(-9, 2), (-9, 5), (2, 7), (4, -1), (9, 4)}
12) xy + 6y = 1
A) Not a function B) Function
A) y is a function of x B) y is not a function of x
7) {(-7, -1), (-3, -6), (-2, -7), (2, -2)}
13) |x| - y = 6
A) Function B) Not a function
A) y is a function of x B) y is not a function of x
8) {(-4, -1), (-3, 7), (2, -8), (2, -9)}
4 Evaluate a Function
A) Not a function B) Function
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
9) {(-6, 6), (-1, 2), (2, -3), (5, 5)}
A) Function B) Not a function Evaluate the function at the given value of the independent variable and simplify.
1) f(x) = 2x + 4; f(6)
10) {(-3, -8), (3, 6), (5, -5), (7, -6), (10, 6)} A) 16 B) 36 C) 8 D) 6
A) Function B) Not a function
2) f(x) = x2 - 4; f(x + 3)
3 Determine Whether an Equation Represents a Function A) x2 + 6x + 5 B) x2 + 9 C) x2 + 6x + 9 D) x2 - 1
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
3) f(x) = 3x2 - 4x + 2; f(x - 1)
Determine whether the equation defines y as a function of x. A) 3x2 - 10x + 9 B) -10x2 + 3x + 9 C) 3x2 - 10x + 1 D) 3x2 + 2x + 1
1) x + y = 49
A) y is a function of x B) y is not a function of x 4) g(x) = 3x + 1; g(x + 1)
1
A) 3x + 4 B) 3x + 1 C) 3x - 1 D) x+1
2) 5x + 7y = 8 3
A) y is a function of x B) y is not a function of x
5) h(x) = x - 11 ; h(15)
3) x2 + y = 25 A) 4 B) -26 C) 26 D) -4
A) y is a function of x B) y is not a function of x
6) f(x) = x + 19; f(-3)
4) x + y 2 = 1 A) 4 B) -4 C) 2 D) not a real number
A) y is a function of x B) y is not a function of x
x2 - 3
7) f(x) = ; f(2)
5) x2 + y 2 = 36 x3 - 6x
A) y is a function of x B) y is not a function of x 1 1 1
A) - B) C) D) - 1
4 8 2
6) y 2 = 6x
A) y is a function of x B) y is not a function of x
x3 + 8
8) f(x) = ; f(5)
x2 - 4
7) x = y 2
A) y is a function of x B) y is not a function of x 19 133 125 11
A) B) C) D)
3 25 21 7
8) y = x3
A) y is a function of x B) y is not a function of x


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Solve the problem. 5 Graph Functions by Plotting Points
9) The function P(x) = 0.65x - 57 models the relationship between the number of pretzels x that a certain
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
vendor sells and the profit the vendor makes. Find P(1000), the profit the vendor makes from selling 1000
pretzels. Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the
A) $593 B) $650 C) $707 D) $943 graph of f.
1) f(x) = x, g(x) = x + 1
10) The total cost in dollars for a certain company to produce x empty jars to be used by a jelly producer is y
given by the function C(x) = 0.3x + 27,000. Find C(90,000), the cost of producing 90,000 jars. 6
A) $54,000 B) $27,000 C) $27.30 D) $90,027 5
4
3
2
1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x
-1
-2
-3
-4
-5
-6

A) g shifts the graph of f vertically up 1 unit B) g shifts the graph of f vertically down 1 unit
y y
6 6
5 5
4 4
3 3
2 2
1 1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x
-1 -1
-2 -2
-3 -3
-4 -4
-5 -5
-6 -6

C) g shifts the graph of f vertically down 1 unit D) g shifts the graph of f vertically up 1 unit
y y
6 6
5 5
4 4
3 3
2 2
1 1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x
-1 -1
-2 -2
-3 -3
-4 -4
-5 -5
-6 -6




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2) f(x) = x, g(x) = x - 4 3) f(x) = -4x, g(x) = -4x - 4
y y
6 6
5 5
4 4
3 3
2 2
1 1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x
-1 -1
-2 -2
-3 -3
-4 -4
-5 -5
-6 -6

A) g shifts the graph of f vertically down 4 units B) g shifts the graph of f vertically down 4 units A) g shifts the graph of f vertically down 4 units B) g shifts the graph of f vertically down 4 units
y y y y
6 6 6 6
5 5 5 5
4 4 4 4
3 3 3 3
2 2 2 2
1 1 1 1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x
-1 -1 -1 -1
-2 -2 -2 -2
-3 -3 -3 -3
-4 -4 -4 -4
-5 -5 -5 -5
-6 -6 -6 -6

C) g shifts the graph of f vertically up 4 units D) g shifts the graph of f vertically up 4 units C) g shifts the graph of f vertically up 4 units D) g shifts the graph of f vertically up 4 units
y y y y
6 6 6 6
5 5 5 5
4 4 4 4
3 3 3 3
2 2 2 2
1 1 1 1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x
-1 -1 -1 -1
-2 -2 -2 -2
-3 -3 -3 -3
-4 -4 -4 -4
-5 -5 -5 -5
-6 -6 -6 -6




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