the graph of the parent function $f(x) = x^3$ is translated to form $g(x) = (x - 7)^3 + 9$. the point $(0…

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 $g(x)$?\n○ $(7, 9)$\n○ $(-7, 9)$\n○ $(9, 7)$\n○ $(9, -7)$
Answer
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))