Question

How do you find the domain and range of `y=-3sin(1/2)x`?

Answer 1

Domain: all reals x
Range: `-3 <= y <= 3`

Explanation:

`y=-3sin(x/2)`
The amplitude is 3
The period (T) = `(2pi)/n = (2pi)/(1/2) = 4pi`

Now you can graph the equation like below.

graph{-3sin(x/2) [-10, 10, -5, 5]}

You will notice then that:
Domain: all reals x
Range: `-3 <= y <= 3`

For the range, a tip is that for the range of the sine or cosine function, the range is always between the positive and negative amplitude.