# What is the domain and range of y = (arccos(x+3))/4?

Dec 2, 2017

The domain is $- 4 \le x \le - 2$ and the range is $0 \le y \le \frac{\pi}{4}$.

#### Explanation:

The ordinary domain and range of arccosine are
$- 1 \le x \le 1$ and $0 \le y \le \pi$, respectively.

The given function, $\arccos \frac{x + 3}{4}$, is shifted 3 units to the left and scaled by a factor of $\frac{1}{4}$.

The new domain is $- 4 \le x \le - 2$ (shifted 3 units to the left of the original) and the new range is $0 \le y \le \frac{\pi}{4}$.