Answer
The red graph is the result.
Domain: $(-\infty,\infty)$
Range: $(-\infty,\infty)$
Work Step by Step
Starting with the graph of $y=x^{3},$
vertically shift upward 1 unit.
Plot several points of $y=x^{3}$,
shift each up by 1 and join with a smooth curve .
Reading from the graph,
Domain: $(-\infty,\infty)$
Range: $(-\infty,\infty)$
