Question

What is the range of `y = 3 cos 4x`?

Answer 1

`-3<=y<=3`

Explanation:

The range is the list of all values that you get when applying the domain (the list of all allowable `x` values).

In the equation `y=3cos4x`, it's the number 3 that is the thing that will affect the range (for working with range, we don't care about the 4 - that deals with how often the graph repeats).

For `y=cosx`, the range is `-1<=y<=1`. The 3 will make the maximum and minimum three times bigger, and so the range is:

`-3<=y<=3`

And we can see that in the graph (the two horizontal lines help to show the range maximum and minimum):

graph{(y-3cos(4x))(y-0x+3)(y-0x-3)=0 [-10, 10, -5, 5]}