Ch. 2 Functions and Their Graphs
2.1 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)
4 → 20
7 → 35
10 → 50
13 → 65
A) function B) function C) not a function
domain: {4, 7, 10, 13} domain:{20, 35, 50, 65}
range: {20, 35, 50, 65} range: {4, 7, 10, 13}
2)
Alice snake
Brad cat
Carl dog
A) function B) function C) not a function
domain: {Alice, Brad, Carl} domain: {snake, cat, dog}
range: {snake, cat, dog} range: {Alice, Brad, Carl}
3)
Alice cat
Brad dog
Carl
A) function B) function C) not a function
domain: {Alice, Brad, Carl} domain: {cat, dog}
range: {cat, dog} range: {Alice, Brad, Carl}
4) {(-2, -7), (0, 5), (5, 0), (6, -1)}
A) function B) function C) not a function
domain: {-2, 0, 5, 6} domain: {-7, 5, 0, -1}
range: {-7, 5, 0, -1} range: {-2, 0, 5, 6}
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}
6) {(-3, 11), (-2, 6), (0, 2), (2, 6), (4, 18)}
A) function B) function C) not a function
domain: {-3, -2, 0, 2, 4} domain: {11, 6, 2, 18}
range: {11, 6, 2, 18} range: {-3, -2, 0, 2, 4}
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9
7) {(5.88, 7.58), (5.888, -7.6), ( , 0), (1.29, -5)}
7
A) function
9
domain: {5.88, 5.888, , 1.29}
7
range: {7.58, -7.6, 0, -5}
B) function
domain: {7.58, -7.6, 0, -5}
9
range: {5.88, 5.888, , 1.29}
7
C) not a function
Determine whether the equation defines y as a function of x.
8) y = x4
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 = 6 - x2
A) function B) not a function
12) y = ± 1 - 5x
A) function B) not a function
13) x = y 2
A) function B) not a function
14) y 2 + x = 2
A) function B) not a function
15) y = 4x2 - 9x + 9
A) function B) not a function
5x - 1
16) y =
x+1
A) function B) not a function
17) x2 - 4y 2 = 1
A) function B) not a function
18) x - 4y = 5
A) function B) not a function
19) -9x + x2 - 97 = y
A) function B) not a function
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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(-4) when f(x) = x2 - 3x + 1.
A) 29 B) 27 C) 3 D) 5
x2 - 8
2) Find f(1) when f(x) = .
x-2
7
A) 7 B) - 9 C) - 1 D) -
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 + 1.
A) 3x2 + 4x + 1 B) -3x2 + 4x - 1 C) 3x2 + 4x - 1 D) -3x2 + 4x + 1
x
6) Find f(-x) when f(x) = .
2
x +8
-x -x x -x
A) B) C) D)
2
x +8 2
x -8 2
-x + 8 -x2 + 8
7) Find -f(x) when f(x) = 2x2 + 5x + 2.
A) -2x2 - 5x - 2 B) 2x2 - 5x + 2 C) 2x2 - 5x - 2 D) -2x2 - 5x + 2
8) Find -f(x) when f(x) = |x| + 9.
A) -|x| - 9 B) |-x| + 9 C) -|x| + 9 D) |-x| - 9
9) Find f(x - 1) when f(x) = 5x2 + 5x - 6.
A) 5x2 - 5x - 6 B) -5x2 + 5x - 6 C) 5x2 - 5x + 4 D) 5x2 - 25x + 4
x2 - 4
10) Find f(x + 1) when f(x) = .
x+4
x2 + 2x - 3 x2 + 2x + 5 x2 + 2x - 3 x2 - 3
A) B) C) D)
x+5 x+5 x-3 x+5
11) Find f(-x) when f(x) = 2x2 - 2x - 4.
A) 2x2 + 2x - 4 B) -2x2 + 2x - 4 C) -2x2 + 2x + 4 D) 2x2 + 2x + 4
12) Find f(2x) when f(x) = 9x2 - 7x.
A) 36x2 - 14x B) 2 9x2 - 7x C) 18x2 - 14x D) 18x2 - 28x
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