Find the average rate of change of a function that contains the points (-2,3) and (2,5).

The average rate of change of a function between two points is the same that the slope of the line passes through these points  (secant line). 

average rate of change=slope of the secant line

Given two points (x₁,y₁) and (x₂,y₂), the slope of the line passes through these points will be:
m=(y₂-y₁)/(x₂-x₁)
(-2,3)
(2,5)

m=(5-3)/(2+2)=2/4=1/2

the average rate of change would be 1/2.