Answer
$y= x^3-4$
Work Step by Step
In order to find the answer, we will have to recall the following some point about the graph of $y=f(x)$.
a) The graph of the function $y=-f(x)$ involves a reflection about the $x$-axis of the original function $f(x)$.
b) The graph of the function $y=f(x)+a$ defines a vertical shift of $|a|$ units upward when $a \gt 0$, and downward side when $a\lt 0$ of the original function $f(x)$.
c) The graph of $y=f(x-p)$ defines a horizontal shift of $|p|$ units to the right when $p \gt 0$, and to the left when $p \lt 0$ of the original function $f(x)$.
(d) The graph of $y=k\cdot f(x)$ can be obtained a vertical stretch when $k\gt 1$ or compression when $0\lt k \lt1$) of the original function $f(x)$.
As mentioned in point $(b)$, the resulting graph would attain a $4$-unit shift downward of the original function $f(x)$ and $a=-4$.
So, we have new function as: $y=f(x)+a \\ y= x^3-4$
