Question

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.

Answer 1

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

Answer 2

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

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 =
`(y_2-y_1)/(x_2-x_1)`

From x=0 to x=1, the rate of change of function=
`(2-1)/(1-0)=1`

From x=1 to x=2, the rate of change of function=
`(4-2)/(2-1)=2`

From x=2 to x=3, the rate of change of function=
`(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.