Compare the graph of the following function with the graph of $f ( x ) = x ^ { 3 }$.
$y = [ 5 ( x + 10 ) ] ^ { 3 }$
A) vertical shift of 10 units up
B) vertical shift of 10 units up horizontal shrink of $\frac { 1 } { 5 }$ units
C) horizontal shift of 10 units to the left horizontal shrink of $\frac { 1 } { 125 }$ units
D) horizontal shift of 10 units to the left horizontal stretch of $\frac { 1 } { 5 }$ units
E) horizontal shift of 10 units to the left vertical shift of 5 units up

Question

Quizplus · Accepted Answer

The correct transformation involves a horizontal shift of 10 units to the left, due to the "(x + 10)" inside the cube, and a horizontal shrink by a factor of $\frac{1}{125}$, which is the cube of the coefficient 5 outside the parentheses, not affecting the horizontal scale directly but the overall scale of the function's output.

Compare the Graph of the Following Function with the Graph f(x)=x3f ( x ) = x ^ { 3 }f(x)=x3

Compare the Graph of the Following Function with the Graph $f ( x ) = x ^ { 3 }$