1. Periodic Functions; Stretching and Translating Graphs
Sec. 4.4

2. Objective
To determine periodicity and amplitude from graphs, to stretch and shrink graphs both vertically and horizontally, and to translate graphs

3. Definitions
Periodic Function: A continuing function whose x and y values that repeat periodically

4. Examples Graphically

5. Examples Graphically

6. A function f is periodic if there is a positive number p, called a period of f, such that:
f(x+p)=f(x)

7. Parts of the periodic funtion
Period: a horizontal distance that a full cycle of a function takes
Amplitude: The measure of a vertical distance of a function and is calculated by:

8. Changing the period and the Amplitude of a periodic function.
If period function has a period p and amplitude A, then:
y= nf(x) has period p and amplitude of nA
y= f(nx) has period p/n and amplitude of A.

9. Example of Periodic Function

10. Page 142
Please refer to the pink table on top of page 142 for the summary of the points discussed in class.

11. Homework
Sec 4.4
Part 1: #1-5 all