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

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

Answer 2

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