# What is the domain and range of y=-|x|-6?

Dec 2, 2017

The domain is $x \setminus \in \mathbb{R}$. The range is $y \le - 6$.

#### Explanation:

The domain of $y = | x |$ is $x \setminus \in \mathbb{R}$.
The range of $y = | x |$ is $y \ge 0$.

The domain of $y = - | x | - 6$ is the same because none of the transformations impact the domain in this case.

The range of $y = - | x | - 6$ is $y \le - 6$ because we take the parent function and reflect it over the $x$-axis and then shift it down 6 units. Reflecting changes the range to $y \le 0$, shifting down makes the new range $y \le - 6$.