Compare the graph of the following function with the graph of $f ( x ) = | x |$.
$y = \left| \frac { 4 } { 9 } x \right|$
A) vertical shift of $\frac { 4 } { 9 }$ units up
B) horizontal stretch of $\frac { 9 } { 4 }$ units
C) vertical shrink of $\frac { 4 } { 9 }$ units
D) horizontal shrink of $\frac { 4 } { 9 }$ units vertical shift of $\frac { 9 } { 4 }$ units
E) horizontal shrink of $\frac { 4 } { 9 }$ units

Question

Quizplus · Accepted Answer

The function $y = \left| \frac { 4 } { 9 } x \right|$ represents a horizontal stretch of the graph of $f(x) = |x|$ by a factor of $\frac { 9 } { 4 }$, because the coefficient $\frac { 4 } { 9 }$ inside the absolute value affects the x-values, making them $\frac { 9 } { 4 }$ times wider to achieve the same y-values as the original function.

Compare the Graph of the Following Function with the Graph f(x)=∣x∣f ( x ) = | x |f(x)=∣x∣

Compare the Graph of the Following Function with the Graph $f ( x ) = | x |$