Answer
The red graph is the result.
Domain: $(-\infty,\infty)$
Range: $[-3,\infty)$
Work Step by Step
Starting with the graph of $y=|x|$
1. horizontally shift to the left 1 unit to obtain ... $y=|x+1|$
2. vertically stretch by a factor of 3 to obtain ... $y=3|x+1|$
3. vertically shift downward 3 units to obtain ... $y=3|x+1|-3$
Plot several points of $y=|x|,$
perform the transformations 1-3 on each,
and join (red on the image).
Reading from the graph,
Domain: $(-\infty,\infty)$
Range: $[-3,\infty)$