For function f(x) = x^2 - 3x + 2
The question is:
Find the average rate of change for this function between the points
(x,f(x)) and (x + h, f(x + h)).
How would you do this?
The (average) rate of change is how much it has changed, divided by the "time" it took to change.
The value of the function has changed from f(x) to f(x+h) so it has changed by f(x+h)- f(x). It did that while x changed from x to x+ h or while x changed by h.
The rate of change is $\displaystyle \frac{f(x+h)- f(x)}{h}$.