Question

How do you find the domain and range of `-3 cos x`?

Answer 1

Domain = `RR`.
Rangge = `[-3,3]`

Explanation:

Any general cosine graph of the form `y=AsinBx` has amplitude of `A` (maximum vertical displacement from the rest position), and period `T=(2pi)/B` representing the amount of units on the x-axis for 1 complete cycle of the graph to take place.

So in this particular case, `A=-3 and T=2pi`.

So the domain being all possible x-values allowed is all real numbers `RR`, and the range being all possible y-values allowed is all y-values between `-3 and 3`, including the endpoints, ie the closed interval `[-3,3]`.