How do you use transformation to graph the cosine function and determine the amplitude and period of y=3cos(-1/2x)?

1 Answer
Sep 21, 2017

Cosine is an even function, so cos(-x) = cosx

i.e. cos(-x/2) = cos(x/2)

Now, the period of cosx is 2pi radians

Hence, as x/2 is a horizontal stretch of factor 2 our period is 4pi radians

Also, -1 <= cos(x/2) <= 1....i.e. amplitude 1

Hence, -3 <= 3cos(x/2) <= 3...i.e. amplitude 3

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