Question

Which statement best explains whether the data in the following table represents a linear or nonlinear function?

x y
−4 4
−1 2.5
0 2
4 4

A -The table represents a nonlinear function because the graph shows a rate of change that is decreasing.

B -The table represents a linear function because the graph shows a rate of change that is increasing.

C -The table represents a nonlinear function because the graph does not show a constant rate of change.

D -The table represents a linear function because the graph shows a constant rate of change.

Answer 1

C -The table represents a nonlinear function because the graph does not show a constant rate of change.

Explanation:

You want to know if the table represents a linear function.

Linear function

A linear function graphs as a straight line. It will have either a zero slope, meaning all y-values are the same, or it will have a non-zero slope. In the latter case, no two y-values are the same.

Application

Your table shows two y-values the same, and different from the others. This cannot be a linear function.

The table represents a nonlinear function, because the rate of change is not constant.