Answer
Refer to the curve in Black in Graph I
Work Step by Step
For $f(x) = \frac{1}{2}x^3 - 4$
when
$x = 2, y = 0;$
$x = 0, y = -4;$
$x = -2, y = -8;$
As seen, $f(x) = \frac{1}{2}x^3 - 4$ is the vertical shrinking by half and the vertical translation down by 4 units of $f(x) = x^3.$
Domain = $(-\infty, \infty)$
Range = $(-\infty, \infty)$
