Answer
the graph is in the picture.
Work Step by Step
if $x\lt-1$ then $g(x)=|-x-1|=-x-1$
if $-1\leq x\lt 0$ then $g(x)=|-x-1|=x+1$
if $0\leq x\lt 1$ then $g(x)=|x-1|=-x+1$
if $1\leq x$ then $g(x)=|x-1|=x-1$
and the graph is in the picture.