Question

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

x −2 −1 0 1 2
y −4 −2 0 2 −2

A - The table represents a nonlinear function because there is not a constant rate of change in the output values.
B - The table represents a nonlinear function because there is not a constant rate of change in the input and output values.
C - The table represents a linear function because there is a constant rate of change in the input and output values.
D - The table represents a linear function because there is not a constant rate of change in the input and output values.

Answer 1

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

Step-by-step explanation:

The table represents a nonlinear function because there is not a constant rate of change in the output values.

In a linear function, the output values change at a constant rate as the input values increase or decrease. However, in this table, the output values do not change at a constant rate.

For example, when x changes from -2 to -1, the corresponding y value changes from -4 to -2, which is a rate of change of 2.

But when x changes from 1 to 2, the corresponding y value changes from 2 to -2, which is a rate of change of -4. Since the rate of change is not constant, the function is nonlinear.