# What is the domain and range of  y =abs(x+4)?

Feb 2, 2016

Domain: all Real values ($\mathbb{R}$)
Range: all Real values $\ge 0$ i.e. $\left[0 , + \infty\right) |$
$\left\mid x + 4 \right\mid$ is defined for all Real values of $x$ (actually it's defined for all Complex values too)
$\left\mid x + 4 \right\mid$ has a minimum value of $0$ (when $x = - 4$) has no upper limit on its size
Therefore the Range is $\left[0 , + \infty\right)$