Question

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

Answer 1

The average rate of change can be found by striking a line between the two endpoints and finding the slope thereof:


`ROC_(ave)=m_(1-2)`

`m_(1-2) = (f(x_2)-f(x_1))/(x_2-x_1) = (f(3)-f(1))/(3-1)`

Solve for f(3) & f(1), substitute into the slope formula and compute.


`m_(1-2) = (9-3)/(3-1)`


`m_(1-2) = (6)/(2) = 3`