Linear and nonlinear functions worksheet

Grade 8 math, Common Core 8.F.A.3. 10 problems with an answer key and worked steps. Free to print, and you can make new problems any time.

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Linear and nonlinear functions

Grade 8 math, Common Core 8.F.A.3

Is each function linear or nonlinear? Explain.

1.
y = x³
2.
Is the function in the table linear or nonlinear?
x 1 2 3 4
y 1 4 9 16
3.
Is the function in the table linear or nonlinear?
x 1 2 3 4
y −1 2 7 14
4.
Is the function in the table linear or nonlinear?
x 1 2 3 4
y 5 8 11 14
5.
Is the function in the table linear or nonlinear?
x 1 2 3 4
y 7 10 15 22
6.
Is the function in the table linear or nonlinear?
x 1 2 3 4
y 5 10 15 20
7.
y = 3 + 5x
8.
6x + y = 6
9.
y = 9x
10.
5x + y = 4

x	1	2	3	4
y	1	4	9	16

x	1	2	3	4
y	−1	2	7	14

x	1	2	3	4
y	5	8	11	14

x	1	2	3	4
y	7	10	15	22

x	1	2	3	4
y	5	10	15	20

Answer key: Linear and nonlinear functions

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

1. Nonlinear. It has an x³ term.
2. Nonlinear. y goes up by 3, then 5, then 7.
3. Nonlinear. y goes up by 3, then 5, then 7.
4. Linear. y goes up by 3 each time.
5. Nonlinear. y goes up by 3, then 5, then 7.
6. Linear. y goes up by 5 each time.
7. Linear. It can be written y = 5x + 3.
8. Linear. It can be written y = −6x + 6.
9. Nonlinear. x is in the denominator.
10. Linear. It can be written y = −5x + 4.

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About linear and nonlinear functions

A linear function has a constant rate of change, so its graph is a straight line and its equation can be written y = mx + b. A nonlinear function changes at different rates: its graph curves. Equations with x², x³, x in a denominator or x as an exponent are nonlinear.

Example 1

y = 3x

Answer: Nonlinear. x is in the denominator.

Example 2

2x + y = 3

Answer: Linear. It can be written y = −2x + 3.

Example 3

y = 12x

Answer: Linear. It has the form y = mx.

Watch out for

In a table, check whether y changes by the same amount each time x goes up by the same amount.
y = 4 − 3x is linear: it is y = −3x + 4.
Any x², x³ or 1x makes the function nonlinear.

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