1. Section 1.3 More on 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
Inc: (-5, -2)
(0, 2)
And (5, ∞)
Dec: (-∞, -5) (-2, 0) and (2, 5)
Constant:
None

6. Example
Find where the graph is increasing. Where is it decreasing? Where is it constant?
Inc: (2, ∞)
Dec: (-∞, 2)
Constant:
None

7. Example
Find where the graph is increasing. Where is it decreasing? Where is it constant?
Inc: None
Dec: None
Constant:
(-2, 0)
(0, 2)
(2, 4)

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
Relative maximum
Relative maximum
(-2, 2)
(2, 2)
(0, 0)
Relative minimum
(-5, -5)
(5, -5)
Relative minimum
Relative minimum

11. Even and Odd Functions and Symmetry

14. Example
Is this an even or odd function?
Even

15. Example
Is this an even or odd function?
ODD

16. Example
Is this an even or odd function?
ODD

17. Piecewise Functions

19. Example
Find and interpret each of the following. 20 20 32

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
f(x + h) = 2(x + h) + 1
= 2x + 2h + 1
D.Q. = 2x + 2h + 1 – (2x + 1) h
D.Q. = 2x + 2h + 1 – 2x – 1 h
D.Q. = 2

26. Example
Find and simplify the expressions if
f(x + h) = (x + h)2 - 4
= x2 + 2hx + h2 - 4
D.Q. = x2 + 2hx + h2 – 4 – (x2 – 4) h
D.Q. = x2 + 2hx + h2 – 4 – x2 + 4 h

27. D.Q. = 2hx +h2 h
D.Q. = 2x + h

28. Example
Find and simplify the expressions if
f(x + h) = (x + h)2 – 2(x + h) + 1
= x2 + 2xh + h2 – 2x – 2h + 1
D.Q.= x2 + 2xh + h2 – 2x – 2h + 1 – x2 + 2x – 1 h
D.Q. = 2xh + h2 – 2h h
= 2x + h - 2

30. Example
$0.59
$0.76

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

32. a.) 6
b.) 3x2 + 6xh
c.) 6x + 3h
d.) 6x

33. (a)
(b)
(c)
(d)