Question

Compare the fallowing functions to determine which has the greater rate of change

Answer 1

Linear functions, like Function 1, have a constant rate of change and its value is equal to the slope.

In the case of y=2x+4, the slope is m=2 so the rate of change is also 2.

In the case of Function 2, we don't know (without calculations) if it is linear or not.

But we can calculate the average rate of change between the points x=-1 and x=2 the same way as calculating the slope between them:

`r=(\Delta y)/(\Delta x)=(y_2-y_1)/(x_2-x_!)=(3-(-6))/(2-(-1))=(9)/(3)=3`

NOTE: If we calculate the slope with point (0,-3) we can confirm this is a linear function with slope m=3.

Answer: Function 2 (r=3) has a greater rate of change than Function 1 (r=2).