Download Algebra 1 Functions Domain and Range Review

Algebra 1
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Functions, Domain, and Range Review
Date________________ Block____
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1) When is a relation a function? What are some
ways to tell if a relation is a function?
2) What is the domain of a function? What is the
range of a function? Given a member of the
domain, how do you find its value in the range?
If f ( x) = −4 x − 7, find...
If f ( x) = −3 x − 2 x + 1, find...
3) a) f (3)
4) a) f (−4)
2
b) f (−7)
b) f (0)
For each question, decide if it is a function. Then find the domain and range in set builder notation.
5)
6)
y
−8
−6
−4
8
6
6
4
4
2
2
−2
2
4
6
8 x
−4
−6
−4
−2
−2
−4
−4
−6
−6
−8
−8
8)
y
−6
−8
−2
7)
−8
y
8
8
6
6
4
4
2
2
2
4
6
8 x
4
6
8 x
2
4
6
8 x
y
8
−2
2
−8
−6
−4
−2
−2
−2
−4
−4
−6
−6
−8
−8
Given the function and a domain, find the range.
9) f ( x) = −7 x + 3, D={-12, -4, 3, 20}
10) f ( x) = 2 x − 2 x + 5, D={-2, -1, 0, 1, 2}
11) f ( x) = 4 x − 1, D={ x| x}
12) f ( x) = 2 x 2 − 6 x + 11, D={ x| x}
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2
Worksheet by Kuta Software LLC
For each question, decide if it is a function. Then find the domain and range in set builder notation.
13)
14)
y
−8
−6
−4
8
6
6
4
4
2
2
−2
2
4
6
8 x
−4
−6
−4
−2
−2
−4
−4
−6
−6
−8
−8
16)
y
−6
−8
−2
15)
−8
y
8
8
6
6
4
4
2
2
2
4
6
8 x
4
6
8 x
2
4
6
8 x
y
8
−2
2
−8
−6
−4
−2
−2
−2
−4
−4
−6
−6
−8
−8
If f ( x) = −3 x − 2, find...
If f ( x) = −11 x − 5 x + 13,
13 find...
17) a) f (0) b) f (4) c) f (−1)
18) a) f (1) b) f (−1) c) f (−4)
2
Given the function and a domain, find the range.
19) f ( x) = −6 x − 1; D={-2, -1, 0, 5}
20) f ( x) = −3 x 2 + x + 8; D={-2, -1, 0, 1}
21) f ( x) = 2 x 2 + 8 x + 3; D={ x| x}
22) f ( x) = −4 x 2 + 8 x + 3; D={ x| x}
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Worksheet by Kuta Software LLC
Answers to Functions, Domain, and Range Review
1) Every input has OAOO output; find an x with more than one y / vertical line test
2) Set of inputs; set of outputs; set x to the domain value and calculate y
3) a) -19 b) 21
4) a) -39 b) 1
5) yes; All real numbers for both: D={ x| x}, R={ y| y}
6) yes; D={ x| x}, R={ y| y ≥ −4}
7) not a function; D={ x| x ≥ −3}, R={ y| y}
8) not a function; D={ x|−2 ≤ x ≤ 6}, R={ y|−6 ≤ y ≤ 2}
9) R={87, 31, -18, -137}
10) R={17, 9, 5}
11) R={ y| y}
12) R={ y| y ≥ 2}
13) yes; D={ x|x}, R={ y|y=-2}
14) no; D={−3}, R={-4, 0, 4}
15) yes; D={ x| x}, R={ y| y}
16) no; D={ x|−5 ≤ x < 5}, R={ y|−2 ≤ y ≤ 2}
17) a) -2 b) -14 c) 1
18) a) -3 b) 7 c) -143
19) R={11, 5, -1, -31}
20) R={-6, 4, 8, 6}
21) R={ y| y ≥ −5}
22) R={ y| y ≤ 7}
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Worksheet by Kuta Software LLC