# What is the domain and range of y= abs(x) - x?

Jun 28, 2018

The domain is $x \in \mathbb{R}$. The range is $y \in \left[0 , + \infty\right)$

#### Explanation:

The domain is $x \in \mathbb{R}$

By definition

$| x |$, $\implies$, $\left\{\begin{matrix}= x \text{ when " x>0 \\ =-x " when } x < 0\end{matrix}\right.$

Therefore,

$y =$, $\left\{\begin{matrix}y = x - x = 0 \text{ when " x>0 \\ y=-x-x=-2x " when " x<0 \\ y=0 " when } x = 0\end{matrix}\right.$

Therefore,

The range is $y \in \left[0 , + \infty\right)$

graph{|x|-x [-11.29, 14.02, -2.84, 9.82]}