1. 4-4 Periodic Functions; Stretching and Translating Graphs

2. Vertical Shift

3. Horizontal Shift

4. Vertical Stretch/Compression

5. Horizontal Stretch/Compression

6. Periodic Function
A function f is periodic if there is a positive number p, called a period of f, such that f(x+p) = f(x) for all x in the domain of f. The smallest period of a periodic function is called the fundamental period of the function.

7. Periodic Function, continued
If a periodic function has a maximum value M and a minimum value m, then the amplitude A of the function is shown above.

8. Notice that a vertical stretching or shrinking affects the amplitude but not the period.
Notice that a horizontal stretching or shrinking affects the period but not the amplitude.

9. Transformations
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10. Transformations, cont.
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11. Transformations, cont.
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12. Transformations, cont.
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13. Transformations, cont.
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14. Transformations, cont.
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15. Transformations, cont.
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