Which statement best explains whether the table represents a linear or nonlinear function?
Input (x) Output (y)
0 1
1 2
2 4
3 16

A- It is a linear function because there is a constant rate of change in both the input and output values.
B- It is a nonlinear function because there is a constant rate of change is both the input and output values.
C- It is a linear function because the output values are increasing at different rates.
D- It is a nonlinear function because the output values are increasing at different rates.

We know that in a linear function , there is always constant rate of change whereas if there is different rates of change of the variables then it is non- linear function.

We know that the rate of change of function =[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

From x=0 to x=1, the rate of change of function=[tex]\frac{2-1}{1-0}=1[/tex]

From x=1 to x=2, the rate of change of function=[tex]\frac{4-2}{2-1}=2[/tex]

From x=2 to x=3, the rate of change of function=[tex]\frac{16-4}{3-2}=12[/tex]

We can see there is increase in function but at different rates.

Therefore, D is the right option. It is a nonlinear function because the output values are increasing at different rates.