Periodic Function Repeats a pattern at regular intervals

· A lot of things in the real world have periodic patterns over time.

In a periodic function f(x + nP) = f(x) If you add even amounts to “x”, you get the same answer for “y.”

A periodic function must repeat the exact same thing over and over again.

Yes No

All trigonometric functions are periodic . Because if you add 360o All trigonometric functions are periodic  Because if you add 360o (or 2 radians), you will get the same result.

Period . How long it takes before. the function starts to. repeat  Period  How long it takes before the function starts to repeat  Also called wavelength

Period = 1 Period = 2 Period = 5

Center  The y-value (often zero) that is in the middle of the graph.  Also called “vertical shift”

Center = 1 Center = 2 Center = .5

Amplitude . How far above and below. the center the graph. extends  Amplitude  How far above and below the center the graph extends  “Height” (though only half) of the graph

Amplitude = .5 Amplitude = 6 Amplitude = 6