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Average rate of change review

Review average rate of change and how to apply it to solve problems.

What is average rate of change?

The average rate of change of function f over the interval axb is given by this expression:
f(b)f(a)ba
It is a measure of how much the function changed per unit, on average, over that interval.
It is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.
Want to learn more about average rate of change? Check out this video.

Finding average rate of change

Example 1: Average rate of change from graph

Let's find the average rate of change of f over the interval 0x9:
We can see from the graph that f(0)=7 and f(9)=3.
Average rate of change=f(9)f(0)90=3(7)9=109

Example 2: Average rate of change from equation

Let's find the rate of change of g(x)=x39x over the interval 1x6.
g(1)=1391=8
g(6)=6396=162
Average rate of change=g(6)g(1)61=162(8)5=34
Problem 1
What is the average rate of change of g over the interval 8x2?
  • Your answer should be
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4

Want to try more problems like this? Check out this exercise.