Answer
The red graph is the result.
Domain: $(-\infty,\infty)$
Range: $[-1,\infty)$
Work Step by Step
Starting with the graph of $y=x^{2},$
vertically shift downward 1 unit.
Plot several points of $y=x^{2}$,
shift each down by 1 and join with a smooth curve.
Reading from the graph,
Domain: $(-\infty,\infty)$
Range: $[-1,\infty)$