Functions worksheet

Grade 8 math, Common Core 8.F.A.1. 10 problems with an answer key and worked steps. Free to print, and you can make new problems any time.

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Functions

Grade 8 math, Common Core 8.F.A.1

Answer each question about functions.

1.
f(x) = 5x − 5. Find f(2).
2.
Is the relation {(5, 1), (4, 7), (6, 6), (3, −3)} a function? Explain.
3.
Does the table show y as a function of x? Explain.
x 1 2 2 3
y 5 6 9 7
4.
Is the relation {(1, 3), (2, 10), (6, −2), (8, 4)} a function? Explain.
5.
f(x) = −5x + 1. Find f(−2).
6.
Is the relation {(7, 8), (1, 0), (8, 4), (5, −4)} a function? Explain.
7.
f(x) = −3x + 4. Find f(−4).
8.
Is the relation {(1, 1), (2, 0), (7, 12), (1, 6)} a function? Explain.
9.
f(x) = −x + 9. Find f(−5).
10.
Does the table show y as a function of x? Explain.
x 1 2 3 4
y 2 7 5 7

x	1	2	2	3
y	5	6	9	7

x	1	2	3	4
y	2	7	5	7

Answer key: Functions

Grade 8 math. Each answer has a few worked steps, to help check the method as well as the answer.

1. 5
f(2) = 5(2) − 5 = 5
2. Yes. Each input has only one output.
3. No. x = 2 has two y-values, 6 and 9.
4. Yes. Each input has only one output.
5. 11
f(−2) = −5(−2) + 1 = 11
6. Yes. Each input has only one output.
7. 16
f(−4) = −3(−4) + 4 = 16
8. No. The input 1 has two outputs, 1 and 6.
9. 14
f(−5) = −1(−5) + 9 = 14
10. Yes. Each x-value has one y-value.

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About functions

A function is a rule that gives exactly one output for each input. A relation is not a function if any input has two different outputs. In a table or list of pairs, look for an x-value that appears twice with different y-values. In function notation, f(4) means the output when the input is 4.

Worked example 1

f(x) = 2x − 3. Find f(−1).

Step 1.f(−1) = 2(−1) − 3 = −5

Answer: −5

Worked example 2

f(x) = −x − 7. Find f(4).

Step 1.f(4) = −1(4) − 7 = −11

Answer: −11

Worked example 3

f(x) = −2x + 5. Find f(−3).

Step 1.f(−3) = −2(−3) + 5 = 11

Answer: 11

Watch out for

An input can appear twice only if it has the same output both times.
Two different inputs can share an output: that is still a function.
To find f(4), replace every x in the rule with 4.

Practice functions online

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