1. Use Graphs of Functions
3.12
Use Graphs of Functions
Vocabulary
For a function f, between any two points (x1, f (x1)) and (x2, f (x2)) is the slope of the line through the two points.
Average Rate
of Change

2. Use Graphs of Functions
3.12
Use Graphs of Functions
Example 1
Find an average rate of change
Find the average rate of change of
Average rate of change of f from x1 = -1 to x2 = 1:
Average rate of change of f from x1 = 1 to x2 = 2:

3. Use Graphs of Functions
3.12
Use Graphs of Functions
Checkpoint. Find the average rate of change of the function from x1 = -1 to x2 = 0.

4. Use Graphs of Functions
3.12
Use Graphs of Functions
Example 2
Compare average rates of change
Compare the average rates of change of the functions from x1 = -3 to x2 = 0.
The function is ____________. So the rate of change, _____, is constant. The average rate of change of f from x1 = -3 to x2 = 0 is _____.
linear -1 -1
Average rate of change of g from x1 = -3 to x2 = 0:
Average rate of change of f from x1 = -3 to x2 = 0:

5. Use Graphs of Functions
3.12
Use Graphs of Functions
Example 3
Solve an equation using a Graph
Method 2
Solve the equation by finding the intersection of two graphs. The solution will be the ___________ of the intersection points.
x-values
Graph both sides of the equation and find the points of intersection. 6 2 -2 -6 -2
The solutions are _____, _____, and _____. 2

6. Use Graphs of Functions
3.12
Use Graphs of Functions
Checkpoint. Solve the equation by graphing. -2
The solutions are _____, and _____.

7. Use Graphs of Functions
3.12
Use Graphs of Functions
Checkpoint. Solve the equation by graphing. 3
The solutions are _____, and about _____.
5.4

8. Use Graphs of Functions
3.12
Use Graphs of Functions