use transformations of the standard cubic function, ( f(x)=x^{3} ), to graph the function ( r(x)=(x…

use transformations of the standard cubic function, ( f(x)=x^{3} ), to graph the function ( r(x)=(x - 5)^{3}+7 ).

use transformations of the standard cubic function, ( f(x)=x^{3} ), to graph the function ( r(x)=(x - 5)^{3}+7 ).

Answer

Explanation:

Step1: Horizontal shift

For the function (y = f(x - h)), it is a horizontal shift of (y = f(x)). If (h>0), shift (h) units to the right. For (r(x)=(x - 5)^{3}+7) compared to (f(x)=x^{3}), when we consider (y=(x - 5)^{3}), it is a shift of (y = x^{3}) (5) units to the right.

Step2: Vertical shift

For the function (y=f(x)+k), it is a vertical shift of (y = f(x)). If (k>0), shift (k) units up. For (r(x)=(x - 5)^{3}+7), after the horizontal shift, we shift (y=(x - 5)^{3}) (7) units up.

Answer:

First, shift the graph of (y = x^{3}) (5) units to the right to get the graph of (y=(x - 5)^{3}). Then, shift the graph of (y=(x - 5)^{3}) (7) units up to obtain the graph of (r(x)=(x - 5)^{3}+7).