Question

The graph of f(x) = 2^x + 1 is shown below. Explain how to find the average rate of change between x = 0 and x = 3.

Answer 1

When you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. f(x) = x2 and f(x + h) = (x + h)2 Therefore, the slope of the secant line between any two points on this function is 2x + h

Answer 2

Average rate of change is a ratio of change on Y-axis to change on X-axis ($\frac{change \ in \ Y}{change \ in \ X} \Rightarrow$ $\frac{f(3)-f(0)}{3-0}=\frac{7-1}{3}=2$.