Question

How do you find the domain & range for -3 cos x?

Answer 1

Domain: `(-oo, oo)`
Range: `[-3, 3]`

Explanation:

The domain is all the valid input values. Since cosine is a periodic function (it repeats), the domain is all real values: `(-oo, oo).`

The `3` says that the cosine function has an amplitude of `3`. The amplitude is the half-height of the wave so that means the range of the function is `[-3, 3]`.

The negative sign in front of the amplitude says that the wave is reversed. This means instead of `(0, 3)`, for the peak, it has `(0, -3)` as the trough if the wave.

Graph of `f(x) = -3cos(x)`:
graph{-3cos(x) [-10, 10, -5, 5]}