Answer
please see image
.
Work Step by Step
$f(x)=x^{3}$
(Using desmos.com) we graph f(x) (blue dashed graph).
By hand, plot the points on the graph of $f(x)$:
(-2,-8), (-1,-1), (0,0), (1,1), (2,8)
and join with a smooth curve.
$r(x)=f(x-2)+1,$
so the graph of $r$ (solid red line)
is obtained from the graph of f by
1. shifting it right by $2$ units (black, dashed),
then
2. raising it by $1$ units (solid red line)
Using the above points, $(x,f(x))$
plot the points
$(x+2$, $f(x)+1)$
and join with a smooth curve.