Question

Which phrase describes a nonlinear function?

A) the area of a circle as a function of the radius
B) the perimeter of a square as a function of the side length
C) the cost of gasoline as a function of the number of gallons purchased
D) the distance traveled by a car moving at constant speed as a function of time

Answer 1

The only non-linear equation from your choices is the area of a circle as it is:

A=πr^2 and if you take the derivative of A you have:

dA/dr=2πr

So the rate of change changes as r changes, it is not constant thus the function has acceleration, so velocity changes.

This is in contrast to any linear equation which is of the form:

y=mx+b now taking the derivative you see that:

dy/dx=m, now m is a constant value, which means that there is no acceleration and the velocity remains constant.