Question

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

Answer 1

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

:)>