# What is the domain and range of y=|x+13|?

Jul 18, 2017

Domain: $\left(- \infty , + \infty\right)$
Range: $\left[0 , + \infty\right)$

#### Explanation:

$y = \left\mid x + 13 \right\mid$

$y$ is defined $\forall x \in \mathbb{R}$

Hence the domain of $y$ is $\left(- \infty , + \infty\right)$

$y \ge 0 \forall x \in \mathbb{R}$

$y$ has no finite upper bound

${y}_{\min} = 0$ at $x = - 13$

Hence the range of $y$ is $\left[0 , + \infty\right)$

This can be seen by the graph of $y$ below.

graph{abs(x+13) [-81.2, 50.45, -32.64, 33.26]}