Question

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 $g(x)$?
○ $(7, 9)$
○ $(-7, 9)$
○ $(9, 7)$
○ $(9, -7)$

Explanation:

Step1: Recall translation rules

For a function \( y = f(x - h) + k \), the graph is shifted \( h \) units right and \( k \) units up from \( y = f(x) \). Here, \( f(x)=x^3 \), \( g(x)=(x - 7)^3+9 \), so \( h = 7 \), \( k = 9 \).

Step2: Apply to point \((0,0)\)

To find the corresponding point on \( g(x) \), add \( h \) to the \( x \)-coordinate and \( k \) to the \( y \)-coordinate of \((0,0)\). So new \( x \)-coordinate: \( 0 + 7 = 7 \), new \( y \)-coordinate: \( 0 + 9 = 9 \).

Answer:

A. \((7, 9)\)