1. Unit 3
Functions

2. Average Rate of Change: Increasing and Decreasing Functions
4.4
Average Rate of Change: Increasing and Decreasing Functions

3. Essential Question:
How can I determine the average rate of a function?

4. Determine the Domain and Range
f(x) = 2x2 + 3
Domain: x   Range: y ≥ 3
f(x) = |x + 3|
Domain: x   Range: y ≥ 0
Domain: x ≥ 1 Range: y ≥ -2

5. Where is the graph increasing, decreasing or constant?
Velocity (m/s)
Time (seconds) 5 8

6. Where is the graph increasing, decreasing or constant?
f(x) = x3
f(x) = x3 – 3x
f(x) = x2 – 4x – 2

7. What does the slope represent?
Average Velocity
position
(x1, f(x1))
(x0, f(x0))
time

8. Average Rate of Change
Describes how much a nonlinear function changes over a given interval
Used for function that model how quickly a given amount increase or decrease
Example:
Revenue
Changes in temperatures
Traveling speed
Etc…

9. Average Rate of Change:
Average Rate of Change between x = a and x = b:

10. Let f(x) = 3x2 – 2 Find Average Rate of Change [1, 7] Given: y = 1/2x2

11. Determine the Average Rate of change from 1991 to 1994 and compare it to the change from 1995 to 1997.
Year
Population
1990
624
1991
856
1992
1336
1993
1578
1994
1591
1995
1483
1996
994
1997
826
1998
801
1999
745
Sketch the graph, when is the function increasing or decreasing?

12. Example
If an object is dropped from a height of 3,000ft, its distance above the ground after t seconds is given by the function h(t) = t2. Find the object’s average speed for
A) between 1.5 and 2.5 seconds
B) between 5 and 10 seconds

13. Revisiting the Essential Question:
How can I determine the average rate of a function?

14. Homework 4.4
Pg 245: 1 – 6, 16 – 26 even