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

Domain: $x \in \mathbb{R}$
Range: $- 4 \ge y \ge 4$

#### Explanation:

The domain is the list of all allowable $x$ values - that is to say - it results in $y$ values that are defined.

With the function $\cos$, it's a sinusoidal graph that cycles around the $x$-axis:

graph{4cosx}

and so the domain is all reals, or $x \in \mathbb{R}$

The range is the list of all the values generated from the domain.

In this case, the resulting $y$ values cycle between 4 and $- 4$, and so the range is $- 4 \ge y \ge 4$