4-4 Periodic Functions; Stretching and Translating Graphs

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Presentation transcript:

4-4 Periodic Functions; Stretching and Translating Graphs

Vertical Shift

Horizontal Shift

Vertical Stretch/Compression

Horizontal Stretch/Compression

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.

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.

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.

Transformations Click for hint!

Transformations, cont. Click for hint!

Transformations, cont. Click for hint!

Transformations, cont. Click for hint!

Transformations, cont. Click for hint!

Transformations, cont. Click for hint!

Transformations, cont. Click for hint!