1. Warm up (-1, 0) (5, 0) x > 2 Find the solutions.
Find the interval of decrease.
(-1, 0) (5, 0)
x > 2

2. Warm-up Find the slope y x
(6,3)
Rise=3-1=2
(2,1)
Run=6-2=4 =

3. Constant Rate of Change
The slope of a nonvertical line is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.
Find the slope between (2, 4) and (4, 8).

4. Rate of Change
The rate of change is the ratio of the change of one quantity to a change in another quantity.
Example:
- The table shows the amount of water evaporating from a swimming pool on a hot day. Find the rate of change in gallons with respect to time.

5. Rate of Change
Where is the greatest rate of change on the graph? What is the value?

6. Partner Practice Calculating rate of change from a table. Example 3

7. Extension

8. Average Rate of Change
The average range of change between any two points (x1,f(x1)) and (x2,f(x2)) is the slope of the line through the 2 points.

9. Example 1
Find the average rate of change of f(x) = 2x2 – 3 when x1= 2 and x2 = 4.

10. Example 2
Find the average rate of change of f(x) = x3 – 3x when x1= -2 and x2 = 0.

11. Walking Task
To begin a class discussion of speed, Dwain and Beth want to stage a walking race down the school hallway. After some experimentation with a stop watch, and using the fact that the flooring tiles measure 1 foot by 1 foot, they decide that the distance of the race should be 40 feet and that they will need about 10 seconds to go 40 feet at a walking pace.
They decide that the race should end in a tie, so that it will be exciting to watch, and finally they make a table showing how their positions will vary over time. Your job is to help Dwain and Beth make sure that they know how they should walk in order to match their plans as closely as possible.

12. Should you connect the dots?
The Data
Time (seconds) 1 2 3 4 5 6 7 8 9 10
Dwain’s position (feet) 12 16 20 24 28 32 36 40
Beth’s position (feet) 15 25 30 35
Draw a graph.
Should you connect the dots?

13. Beth (blue) Dwain (Purple)
Describe how Dwain and Beth should walk in order to match their data.

14. Beth (blue) Dwain (Purple)
What is Beth and Dwain’s average speed from 0 to 3 seconds?

15. Beth (blue) Dwain (Purple)
What is Beth and Dwain’s average speed from 6 to 8 seconds?

16. Beth (blue) Dwain (Purple)
What is Beth and Dwain’s average speed from 0 to 10 seconds?

17. Homework
Practice Worksheet and Coach Page 94