Answer
RECALL:
(1) The graph of the function $y=f(x-h)$ involves a horizontal shift of $|h|$ units (to the right when $h$ is positive, to the left when $h$ is negative) of the parent function $y=f(x)$.
(2) The graph of the function $y=f(x)+k$ involves a vertical shift of $|k|$ units (upward when $k$ is positive, downward when $k$ is negative) of the parent function $y=f(x)$.
The parent function of the given function is $y=x^3$.
The given function can be written as $fx)=(x-3)^3+6$.
Thus, the given function involves a horizontal and a vertical translation of the parent function $y=x^3$.
Therefore, the missing expressions in the given statement (in order) are:
$3$;
$6$
Work Step by Step
RECALL:
(1) The graph of the function $y=f(x-h)$ involves a horizontal shift of $|h|$ units (to the right when $h$ is positive, to the left when $h$ is negative) of the parent function $y=f(x)$.
(2) The graph of the function $y=f(x)+k$ involves a vertical shift of $|k|$ units (upward when $k$ is positive, downward when $k$ is negative) of the parent function $y=f(x)$.
The parent function of the given function is $y=x^3$.
The given function can be written as $fx)=(x-3)^3+6$.
Thus, the given function involves a horizontal and a vertical translation of the parent function $y=x^3$.
Since $h=3$ and $k=6$, then the graph of the given function involves a 3-unit shift to the right and 6-unit shift upward of the parent function $y=x^3$.
Therefore, the missing expressions in the given statement (in order) are:
$3$;
$6$
