Question

graph the equation shown below by transforming the given graph of the parent function.
$y = |2x|$

Explanation:

Step1: Identify parent function

The parent function is $y=|x|$, a V-shaped graph with vertex at $(0,0)$, passing through $(1,1)$ and $(-1,1)$.

Step2: Recognize transformation type

For $y=|2x|$, this is a horizontal compression of $y=|x|$ by a factor of $\frac{1}{2}$. The rule for horizontal scaling: $y=|k x|$ compresses $y=|x|$ horizontally by $\frac{1}{|k|}$ when $|k|>1$.

Step3: Calculate key points

For $y=|2x|$:

• When $x=0$, $y=|2(0)|=0$ → point $(0,0)$
• When $x=1$, $y=|2(1)|=2$ → point $(1,2)$
• When $x=2$, $y=|2(2)|=4$ → point $(2,4)$
• When $x=-1$, $y=|2(-1)|=2$ → point $(-1,2)$
• When $x=-2$, $y=|2(-2)|=4$ → point $(-2,4)$

Step4: Plot and connect points

Plot the calculated points and draw a V-shaped graph with vertex at $(0,0)$, steeper than the parent function $y=|x|$.

Answer:

The graph of $y=|2x|$ is a horizontal compression of the parent absolute value function $y=|x|$ by a factor of $\frac{1}{2}$, forming a V-shape with vertex at $(0,0)$, passing through points such as $(1,2)$, $(2,4)$, $(-1,2)$, $(-2,4)$, and rising/falling twice as steeply as the parent function.