#### Answer

please see image
.

#### Work Step by Step

$f(x)=\sqrt[3]{x}=x^{1/3}$
(Using desmos.com) we graph f(x) (blue dashed graph).
By hand, plot the points on the graph of $f(x)$:
(-8,-2), (-1,-1), (0,0), (1,1), (8,2)
and join with a smooth curve.
$r(x)=\displaystyle \frac{1}{2}f(x+2)-2,$
so the graph of $r$ (solid red line)
is obtained from the graph of f by
1. shifting it left by 2 units (green, dashed)
then
2. vertically shrinking 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
$(x-2,\ \displaystyle \frac{1}{2}f(x)-2 )$
and join with a smooth curve.