IXL | Identify linear and nonlinear functions: tables

The table shows a function. Is the function linear or nonlinear?

x	y
16	19
17	10
18	1

linear

nonlinear

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question

The table shows a function. Is the function linear or nonlinear?

x	y
17	14
18	10
19	0

linear

nonlinear

key idea

A linear function has a constant rate of change. A nonlinear function does not.

A function's rate of change between two points

(

)

and

(

)

is:

–

A function has a constant rate of change if its rate of change is the same between any two points.

solution

To determine whether the function is linear or nonlinear, see whether it has a constant rate of change.

Pick any two rows of the table and calculate the rate of change between them. The first two rows are a good place to start.

Rows 1 and 2:

x	y
17	14
18	10
19	0

Call the values in the first row

and

Call the values in the second row

and

Rate of change

–

Now pick a different pair of rows and calculate the rate of change between them.

Rows 2 and 3:

x	y
17	14
18	10
19	0

Call the values in the second row

and

Call the values in the third row

and

Rate of change

–

The rate of change is not the same for each pair of points. So, the function does not have a constant rate of change.

The function is

nonlinear.

Looking for more? Try these:

Lesson: Linear functions

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Teacher tools

Work it out

Not feeling ready yet? These can help:

W.7Rate of change: tables

DD.1Identify linear and nonlinear functions: graphs and equations

Lesson: Linear functions

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