1. Identifying the Average Rate of Change
Adapted from Walch Education

2. Average of Rate Change
The average rate of change of a function is the rate of change between any two points of a function; it is a measure of how a quantity changes over some interval.
The average can be found by calculating the ratio of the difference of output values to the difference of the corresponding input values, from x = a to x = b. This formula is often referred to as the average rate of change formula.
5.5.3: Identifying the Average Rate of Change

3. Average Rate of Change
Recall that the slope of a linear function is found using the formula
Both formulas are used to find the rate of change between two specific points.
The rate of change of a linear function is always constant, whereas the average rate of change of a quadratic function is not constant.
5.5.3: Identifying the Average Rate of Change

4. Practice # 1
Calculate the average rate of change for the function f(x) = x2 + 6x + 9 between x = 1 and x = 3.
5.5.3: Identifying the Average Rate of Change

5. Evaluate the function for x = 3 and x = 1
f(x) = x2 + 6x + 9
Original function
f(3) = (3)2 + 6(3) + 9
Substitute 3 for x.
f(3) = 36
Simplify.
f(x) = x2 + 6x + 9
Original function
f(1) = (1)2 + 6(1) + 9
Substitute 1 for x.
f(1) = 16
Simplify.
5.5.3: Identifying the Average Rate of Change

6. Use the average rate of change formula
Substitute 1 for a and 3 for b.
Substitute the values for f(3) and f(1).
Simplify.
5.5.3: Identifying the Average Rate of Change

7. You Try.
Use the graph of the function at right to calculate the average rate of change between x = –3 and x = –2.
5.5.3: Identifying the Average Rate of Change

8. Thanks for Watching!
Ms. Dambreville