1. Aim #2.2 What else is there to know about Functions and Their Graphs?

2. Increasing and Decreasing Functions

4. The open intervals describing where functions increase, decrease, or are constant, use x-coordinates and not the y-coordinates.

5. Find where the graph is increasing. Where is it decreasing
Find where the graph is increasing? Where is it decreasing? Where is it constant?
Example

6. Example
Find where the graph is increasing? Where is it decreasing? Where is it constant?

7. Example
Find where the graph is increasing? Where is it decreasing? Where is it constant?

8. Relative Maxima And Relative Minima

10. Where are the relative minimums? Where are the relative maximums?
Why are the maximums and minimums called relative or local?
Example

11. Even and Odd Functions and Symmetry

14. Example
Is this an even or odd function?

15. Example
Is this an even or odd function?

16. Example
Is this an even or odd function?

17. Piecewise Functions

19. Example
Find and interpret each of the following.

20. Example
Graph the following piecewise function.

21. Functions and Difference Quotients

22. See next slide.

23. Continued on the next slide.

25. Example
Find and simplify the expressions if

26. Example
Find and simplify the expressions if

27. Example
Find and simplify the expressions if

29. Example

30. (a)
(b)
(c)
(d)

31. (a)
(b)
(c)
(d)

32. (a)
(b)
(c)
(d)

33. Summary: Answer in complete sentences.
What is the difference between an even and odd function?
How can you identify increasing and decreasing functions?