# What is the domain and range of y=|x-1|-9?

Jan 24, 2018

The domain is $x \in \mathbb{R}$ and the range is $y \ge - 9$.

#### Explanation:

For the function $y = | x |$ the domain is $x \in \mathbb{R}$ and range is $y \ge 0$.

The function $y = | x - 1 | - 9$ is a horizontal shift of $| x |$ by 1 unit to the right and a vertical shift of $| x |$ by 9 units down.

Shifting left or right doesn't impact the domain since it's already all real numbers.

Shifting down 9 units changes the range from $y \ge 0$ to $y \ge - 9$.

Therefore the domain of $y = | x - 1 | - 9$ is $x \in \mathbb{R}$ and the range is $y \ge - 9$.