1. Warm up What is the tenth term of an = 2n + 3? What is the Domain:
Range:
x – ints:
y – int:

2. Review HW

3. Average Rate of Change

4. Rate of Change
Ratio describing how one quantity changes as another quantity changes
Slope can be used to describe it

5. Rate of Change Positive – increases over time
Negative – decreases over time

6. Rate of Change
Linear functions have a constant rate of change, meaning values increase or decrease at the SAME rate over a period of time

7. Rate of Change Horizontal lines have 0 rate of change
Vertical lines have undefined rate of change

8. Rate of Change
The slope of a non-vertical line is the ratio of the vertical change
(change in y) to the horizontal change
(change in x) between any two points
on the line.

9. Rate of Change
Example: Find the slope between
(2, 4) and (4, 8)

10. Rate of Change
Example: The table shows the amount of water evaporating from a swimming pool on a hot day. Find the rate of change between 2 hours and 6 hours.

11. Rate of Change
Example: Where is the greatest rate of change on the graph?
What is the value?

12. Average Rate of Change

13. Ex 1 Find the Average Rate of Change
f(x) = -4x + 10 from [-1, 3].
m = -4

14. Ex 2 Find the Average Rate of Change
f(x) = 2x2 – 3 from [2, 4].

15. You Try!!
Find the average rate of change for
f(x) = x2 + 2 from [-3, 5].

16. A. Find the rate of change from day 1 to 2.
Ex 4 Find the Average Rate of Change
A. Find the rate of change from day 1 to 2.
m = 11
Days (x)
Amount of Bacteria f(x) 1 19 2 30 3 48 4 76 5
121 6
192
B. Find the rate of change from day 2 to 5.

17. Ex 5 Find the Average Rate of Change Households in Millions f(x)
In 2008, about 66 million U.S. households had both landline phones & cell phones. Find the rate of change from 2008 – 2011.
Year (x)
Households in Millions f(x)
2008 66
2009 61
2010 56
2011 51
m = -5
What does this mean?
It decreased 5 million households per year from 2008 – 11.

18. Class Work Handout