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## Algebra 1

### Course: Algebra 1>Unit 8

Lesson 12: Average rate of change word problems

# 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 a, is less than or equal to, x, is less than or equal to, b is given by this expression:
start fraction, f, left parenthesis, b, right parenthesis, minus, f, left parenthesis, a, right parenthesis, divided by, b, minus, a, end fraction
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.

## 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 0, is less than or equal to, x, is less than or equal to, 9:
We can see from the graph that f, left parenthesis, 0, right parenthesis, equals, minus, 7 and f, left parenthesis, 9, right parenthesis, equals, 3.
\begin{aligned} \text{Average rate of change}&=\dfrac{f(9)-f(0)}{9-0} \\\\ &=\dfrac{3-(-7)}{9} \\\\ &=\dfrac{10}{9} \end{aligned}

### Example 2: Average rate of change from equation

Let's find the rate of change of g, left parenthesis, x, right parenthesis, equals, x, cubed, minus, 9, x over the interval 1, is less than or equal to, x, is less than or equal to, 6.
g, left parenthesis, 1, right parenthesis, equals, 1, cubed, minus, 9, dot, 1, equals, minus, 8
g, left parenthesis, 6, right parenthesis, equals, 6, cubed, minus, 9, dot, 6, equals, 162
\begin{aligned} \text{Average rate of change}&=\dfrac{g(6)-g(1)}{6-1} \\\\ &=\dfrac{162-(-8)}{5} \\\\ &=34 \end{aligned}
Problem 1
• Current
What is the average rate of change of g over the interval minus, 8, is less than or equal to, x, is less than or equal to, minus, 2?

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