Translating Sine and Cosine Functions

F.TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

Recall that for any function f, you can graph f(x - h) by translating the graph of f by h units horizontally. You can graph f(x) + k by translating the graph of f by k units vertically.

Each horizontal translation of certain periodic functions is a phase shift.

g(x): horizontal translation of f(x)

h(x): vertical translation of f(x). h(x) = f(x) + k

Translations To refresh your memory on translation, go ahead and click on the link.