Answer
$f(x)=(x-4)^3$
Work Step by Step
RECALL:
(1) The graph of $y=f(x-h)$ involves a horizontal shift of $|h|$ units (to the right when $h \gt 0$, to the left when $h\lt0$) of the parent function $f(x)$.
(2) The graph of $y=f(x)+k$ involves a vertical shift of $|k|$ units (upward when $k \gt 0$, downward when $k\lt0$) of the parent function $f(x)$.
(3) The graph of $y=a \cdot f(x-h)$ involves a vertical stretch or compression (stretch when $a\gt1$, compression when $0\lt a \lt1$) of the parent function $f(x)$.
(4) The graph of $y=-f(x)$ involves a reflection about the $x$-axis of the parent function $f(x)$.
Hence here: $x^3\rightarrow(x-4)^3.$
