Answer
The red graph is the result.
Domain: $(-\infty,0]$
Range: $[-2,\infty)$
Work Step by Step
Starting with the graph of $y=\sqrt{x}$
1. reflect the graph about the $y$ -axis to obtain ... $y=\sqrt{-x}$
2. vertically shift downward 2 units to obtain .... $y=\sqrt{-x}-2$
Plot several points of $y=|x|,$
perform the transformations 1-2 on each,
and join (red on the image).
Reading from the graph,
Domain: $(-\infty,0]$
Range: $[-2,\infty)$
