Question

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


x y
−2 negative 19 over 3
−1 −3
0 1 over 3
1 11 over 3
2 7
The table represents a linear function because the rate of change is constant.
The table represents a linear function because the rate of change is not constant.
The table represents a nonlinear function because the rate of change is constant.
The table represents a nonlinear function because the rate of change is not constant.

Answer 1

The correct statement is: The table represents a nonlinear function because the rate of change is not constant.

In a linear function, the rate of change is constant, which means that the change in the output (y) for each unit change in the input (x) is always the same. In this table, the rate of change is not constant, which means that the change in the output (y) for each unit change in the input (x) varies. Therefore, the function represented by this table is nonlinear.