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Test Bank For College Algebra Concepts Through Functions, 5th Edition by Chapter 1-8
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Test Bank For College Algebra Concepts Through Functions, 5th Edition by Chapter 1-8
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Ch. 1 Functions and Their Graphs1.1 Functions
1 Determine Whether a Relation Represents a Function
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine whether the relation represents a function. If it is a function, state the domain and range.
1)
3 → 12
4 → 16
5 → 20
6 → 24
A) function B) function C) not a function
domain: {3, 4, 5, 6} domain:{12, 16, 20, 24}
range: {12, 16, 20, 24} range: {3, 4, 5, 6}
2)
Bob carrots
Ann peas
Dave squash
A) function
domain: {Bob, Ann, Dave}
range: {carrots, peas, squash}
B) function
domain: {carrots, peas, squash}
range: {Bob, Ann, Dave}
C) not a function
3)
Bob Ms. Lee
Ann Mr. Bar
Dave
A) function B) function C) not a function
domain: {Bob, Ann, Dave} domain: {Ms. Lee, Mr. Bar}
range: {Ms. Lee, Mr. Bar} range: {Bob, Ann, Dave}
4) {(-2, 7), (1, 3), (3, -5), (7, -2)}
A) function B) function C) not a function
domain: {-2, 1, 3, 7} domain: {7, 3, -5, -2}
range: {7, 3, -5, -2} range: {-2, 1, 3, 7}
5) {(5, -2), (1, -1), (1, 0), (2, 1), (10, 3)}
A) function B) function C) not a function
domain: {5, 2, 1, 10} domain: {-2, -1, 0, 1, 3}
range: {-2, -1, 0, 1, 3} range: {5, 2, 1, 10}
Page 1
, 6) {(-4, 17), (-3, 10), (0, 1), (3, 10), (5, 26)}
A) function B) function C) not a function
domain: {-4, -3, 0, 3, 5} domain: {17, 10, 1, 26}
range: {17, 10, 1, 26} range: {-4, -3, 0, 3, 5}
5
7) {(4.22, 11.42), (4.222, -11.4), ( , 0), (0.71, -4)}
7
A) function
5
domain: {4.22, 4.222, , 0.71}
7
range: {11.42, -11.4, 0, -4}
B) function
domain: {11.42, -11.4, 0, -4}
5
range: {4.22, 4.222, , 0.71}
7
C) not a function
Determine whether the equation defines y as a function of x.
8) y = x2
A) function B) not a function
1
9) y =
x
A) function B) not a function
10) y = |x|
A) function B) not a function
11) y 2 = 8 - x2
A) function B) not a function
12) y = ± 1 - 7x
A) function B) not a function
13) x = y 2
A) function B) not a function
14) y 2 + x = 9
A) function B) not a function
15) y = 3x2 - 7x + 9
A) function B) not a function
5x - 3
16) y =
x+1
A) function B) not a function
17) x2 + 2y 2 = 1
A) function B) not a function
Page 2
, 18) x + 7y = 9
A) function B) not a function
19) 9x + x2 - 66 = y
A) function B) not a function
2 Find the Value of a Function
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the value for the function.
1) Find f(-1) when f(x) = x2 - 2x + 6.
A) 9 B) -3 C) -7 D) 5
x2 - 3
2) Find f(2) when f(x) = .
x+1
1 7 4
A) B) C) D) - 1
3 3 3
3) Find f(-9) when f(x) = |x|- 6.
A) 3 B) -15 C) 15 D) -3
4) Find f(7) when f(x) = x2 + 5x.
A) 2 21 B) 74 C) 30 D) 3 6
5) Find f(-x) when f(x) = 3x2 + 4x - 5.
A) 3x2 - 4x - 5 B) -3x2 - 4x + 5 C) 3x2 - 4x + 5 D) -3x2 - 4x - 5
x
6) Find f(-x) when f(x) = .
2
x +4
-x -x x -x
A) B) C) D)
2
x +4 2
x -4 2
-x + 4 -x2 + 4
7) Find -f(x) when f(x) = 2x2 + 5x + 5.
A) -2x2 - 5x - 5 B) 2x2 - 5x + 5 C) 2x2 - 5x - 5 D) -2x2 - 5x + 5
8) Find -f(x) when f(x) = |x| - 2.
A) -|x| + 2 B) |-x| - 2 C) -|x| - 2 D) |-x| + 2
9) Find f(x - 1) when f(x) = 4x2 + 5x - 7.
A) 4x2 - 3x - 8 B) -3x2 + 4x - 8 C) 4x2 - 3x + 2 D) 4x2 - 23x + 2
x2 - 2
10) Find f(x + 1) when f(x) = .
x-4
x2 + 2x - 1 x2 + 2x + 3 x2 + 2x - 1 x2 - 1
A) B) C) D)
x-3 x-3 x+5 x-3
11) Find f(-x) when f(x) = -3x2 - 2x + 4.
A) -3x2 + 2x + 4 B) 3x2 + 2x + 4 C) 3x2 + 2x - 4 D) -3x2 + 2x - 4
Page 3
, 12) Find f(2x) when f(x) = 6x2 + 5x.
A) 24x2 + 10x B) 2 6x2 + 5x C) 12x2 + 10x D) 12x2 + 20x
13) Find f(x + h) when f(x) = 2x2 + 5x - 4.
A) 2x2 + 4xh + 2h2 + 5x + 5h - 4 B) 2x2 + 2h2 + 5x + 5h - 4
C) 2x2 + 2h2 + 9x + 9h - 4 D) 2x2 + 2xh + 2h2 + 5x + 5h - 4
5x + 8
14) Find f(x + h) when f(x) = .
8x - 5
5x + 5h + 8 5x + 5h + 8 5x + 13h 5x + 8h
A) B) C) D)
8x + 8h - 5 8x - 5 8x + 3h 8x - 5h
Solve the problem.
15) If f(x) = 6x3 + 9x2 - x + C and f(2) = 1, what is the value of C?
A) C = -81 B) C = 11 C) C = 15 D) C = 87
x-B
16) If f(x) = , f(2) = 0, and f(4) is undefined, what are the values of A and B?
x-A
A) A = 4, B = 2 B) A = 2, B = 4 C) A = -4, B = -2 D) A = -2, B = -4
x - 5A
17) If f(x) = and f(-5) = -15, what is the value of A?
-5x + 1
A) A = 77 B) A = -77 C) A = -27 D) A = 27
18) If a rock falls from a height of 70 meters on Earth, the height H (in meters) after x seconds is
approximately
H(x) = 70 - 4.9x2 .
What is the height of the rock when x = 1.6 seconds? Round to the nearest hundredth, if necessary.
A) 57.46 m B) 82.54 m C) 62.16 m D) 57.71 m
19) If a rock falls from a height of 80 meters on Earth, the height H (in meters) after x seconds is
approximately
H(x) = 80 - 4.9x2 .
When does the rock strike the ground? Round to the nearest hundredth, if necessary.
A) 4.04 sec B) 16.33 sec C) 1.83 sec D) 3.33 sec
3 Find the Domain of a Function Defined by an Equation
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the domain of the function.
1) f(x) = -4x + 6
A) all real numbers B) {x|x ≥ -6} C) {x|x ≠ 0} D) {x|x > 0}
2) f(x) = x2 + 8
A) all real numbers B) {x|x ≥ -8} C) {x|x > -8} D) {x|x ≠ -8}
x
3) f(x) =
x2 + 6
A) all real numbers B) {x|x ≠ -6} C) {x|x > -6} D) {x|x ≠ 0}
Page 4
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