# What is the domain and range of y= | x - 3 | + 8?

Dec 15, 2015

Domain: $\mathbb{R}$ (all Real numbers)
Range: y>=8; y in RR

#### Explanation:

$y = \left\mid x - 3 \right\mid + 8$
is defined for all Real values of $x$
So the domain is $\mathbb{R}$

Since $\left\mid x - 3 \right\mid \ge 0$
$\textcolor{w h i t e}{\text{XXX}} \left\mid x - 3 \right\mid + 8 \ge 8$
and $y$ is only defined for Rel values $\ge 8$