Answer
Domain: $(-\infty,\infty)$
Range: $(-\infty,0]$
Work Step by Step
The domain of an absolute value function is all real numbers or $(-\infty,\infty)$
The function $f(x)=|x|$ has a range of $[0,\infty)$
So the range of $f(x)=-|x+1|$ is $(-\infty,0]$