Compare the graph of the following function with the graph of $f ( x ) = | x |$.
$$y = \left| \frac { 3 } { 4 } x \right|$$
A) vertical shift of $\frac { 3 } { 4 }$ units up
B) horizontal stretch of $\frac { 4 } { 3 }$ units
C) vertical shrink of $\frac { 3 } { 4 }$ units horizontal shrink of $\frac { 3 } { 4 }$ units
D) vertical shift of $\frac { 4 } { 3 }$ units
E) horizontal shrink of $\frac { 3 } { 4 }$ units

Question

Quizplus · Accepted Answer

The equation $y = |x|$ is the absolute value function. The equation $y = \left| \frac{3}{4}x \right|$ is a vertical shrink of $\frac{3}{4}$ units and horizontal shrink of $\frac{4}{3}$ units of the absolute value function. Therefore, the graphs will have the same shape, but the second graph will be narrower than the first. Thus, the correct choice is B, a horizontal stretch of $\frac{4}{3}$ units.

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 $f ( x ) = | x |$