Question

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

Answer 1

Answer: D- It is a nonlinear function because the output values are increasing at different rates.

Step-by-step explanation:

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 =$\frac{y_2-y_1}{x_2-x_1}$

From x=0 to x=1, the rate of change of function=$\frac{2-1}{1-0}=1$

From x=1 to x=2, the rate of change of function=$\frac{4-2}{2-1}=2$

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

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.

Answer 2

D. It is non-linear because the output values are increasing at different rates