Question

Which two points in the graphed function have an average rate of change of 5?

Answer 1

First of all, a positive average rate of change means that the function is increasing, so the answer can only be A->B or B->C.

The average rate of change is defined as

$A = \dfrac{f(b)-f(a)}{b-a}$

i.e. as the ratio between the vertical and horizontal gain.

In order to go from point A to point B, you gain 1 unit horizontally and 5 units vertically. So, the average rate of change is 5/1=5.

In order to go from point B to point C, you gain 1 unit horizontally and 3 units vertically. So, the average rate of change is 3/1=3.