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.
$h(x)=\displaystyle \frac{1}{2}f(x-2)-1,$
so the graph of $h$ (solid red line)
is obtained from the graph of f by
1. shifting it right by $2$ units (green dashed),
then
2. vertically compressing it by factor $\displaystyle \frac{1}{2} $(black, dashed),
and then
3. lowering it by $1$ units (solid red line)
Using the above points, $(x,f(x))$
plot the points
$(x+2$, $\displaystyle \frac{1}{2}f(x)-1)$
and join with a smooth curve.