# What is the domain and range of x + 3 = |y|?

Sep 19, 2016

$x \in \left[- 3 , \infty\right) \mathmr{and} y \in \left(- \infty , \infty\right)$

#### Explanation:

$| y | = x + 3 \ge 0$. So, $x \ge - 3$.

This equation is the combined equation for the pair of straight

half-lines that make a right angled horizontal V.

The separate equations are.

$y = x + 3 , y \ge 0 \mathmr{and}$

$y = - \left(x + 3\right) , y \le 0$

The right angular terminal is (-3, 0).. They lines are equally

inclined to the x-axis y = 0..

$x \in \left[- 3 , \infty\right) \mathmr{and} y \in \left(- \infty , \infty\right)$