1. Average Rate of Change

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

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

4. 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

5. Rate of Change
Exponential Functions do not have a constant rate of change, meaning that values increase or decrease at different rates over a period of time.

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

7. Average Rate of Change using function notation

8. Ex 1 Find the Average Rate of Change
f(x) = 2x2 – 3 from [2, 4].

9. Ex 2 Find the Average Rate of Change
f(x) = 3x – 2 from 2 ≤ x ≤ 5

10. Ex 3 Find the Average Rate of Change
f(x) = -4x + 10 from x1= -1 x2= 3.
m = -4

11. 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.

12. 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.