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

$- 3 \le y \le 3$

#### 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 $y = 3 \cos 4 x$, 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 $y = \cos x$, the range is $- 1 \le y \le 1$. The 3 will make the maximum and minimum three times bigger, and so the range is:

$- 3 \le y \le 3$

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]}