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