the graph of the parent function $f(x) = x^3$ is translated to form the graph of $g(x) = (x - 4)^3 - 7$. the…

the graph of the parent function $f(x) = x^3$ is translated to form the graph of $g(x) = (x - 4)^3 - 7$. the point $(0, 0)$ on the graph of $f(x)$ corresponds to which point on the graph of $g(x)$?\n○ $(4, -7)$\n○ $(-4, -7)$\n○ $(4, 7)$\n○ $(-4, 7)$

the graph of the parent function $f(x) = x^3$ is translated to form the graph of $g(x) = (x - 4)^3 - 7$. the point $(0, 0)$ on the graph of $f(x)$ corresponds to which point on the graph of $g(x)$?\n○ $(4, -7)$\n○ $(-4, -7)$\n○ $(4, 7)$\n○ $(-4, 7)$

Answer

Explanation:

Step1: Recall translation rules

For a function ( y = f(x - h)+k ), the graph is translated ( h ) units right (if ( h>0 )) and ( k ) units up (if ( k>0 )). Here, ( g(x)=(x - 4)^3-7=f(x - 4)-7 ), so ( h = 4 ) (right translation) and ( k=-7 ) (down translation).

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

To translate the point ((x,y)) on ( f(x) ) to ( g(x) ), we use ( (x + h,y + k) )? Wait, no: if ( g(x)=f(x - h)+k ), then the point ((a,b)) on ( f(x) ) corresponds to ((a + h,b + k))? Wait, let's think again. If ( f(x) ) has a point ((x_0,y_0)), then for ( g(x)=f(x - h)+k ), we set ( x - h=x_0 ) and ( y= y_0 + k ). So ( x=x_0 + h ), ( y=y_0 + k ). For the point ((0,0)) on ( f(x) ), ( x_0 = 0 ), ( y_0 = 0 ). Then ( x=0 + 4=4 ), ( y=0+(-7)=-7 ). So the corresponding point is ((4,-7)).

Answer:

A. ((4, -7))