Question

cubic and cube root functions and equations
the graph of the parent function $f(x)=x^3$ is translated to form $g(x)=(x - 7)^3+9$. the point $(0,0)$ on the graph of $f(x)$ corresponds to which point on the graph of $g(x)$?
$(9, 7)$
$(7, 9)$
$(9,-7)$
$(-7,9)$

Explanation:

Step1: Identify horizontal translation

For $g(x)=(x-7)^3 + 9$, horizontal shift: $x \to x-7$. To map $x=0$ from $f(x)$, solve $x-7=0$ → $x=7$.

Step2: Identify vertical translation

Vertical shift: add 9 to $f(x)$. For $y=0$ from $f(x)$, $y=0+9=9$.

Step3: Combine results

The corresponding point is $(7, 9)$.

Answer:

(7, 9)