Answer
Domain = $\mathbb{R}$,
Range = $\{y\in \mathbb{R}|y\geq 0\}$

Work Step by Step
The graph of
$g(x)=|x+1|$
is obtained by shifting the graph of $f(x)=|x|$
by one unit to the left.
Domain = $\mathbb{R}$,
Range = $\{y\in \mathbb{R}|y\geq 0\}$