Question

graph the equation shown below by transforming the given graph of the parent function.
$y = |3x|$

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 $y=|3x|$, this is a horizontal compression of $y=|x|$ by a factor of $\frac{1}{3}$. The rule for horizontal scaling: $y=|k x|$ compresses $y=|x|$ horizontally by $\frac{1}{|k|}$ when $|k|>1$.

Step3: Find key points for transformed function

• For $x=0$: $y=|3(0)|=0$, so point $(0,0)$ (vertex stays same).
• For $x=1$: $y=|3(1)|=3$, so point $(1,3)$.
• For $x=-1$: $y=|3(-1)|=3$, so point $(-1,3)$.
• For $x=2$: $y=|3(2)|=6$, so point $(2,6)$.
• For $x=-2$: $y=|3(-2)|=6$, so point $(-2,6)$.

Step4: Plot and connect points

Draw a V-shaped graph with vertex at $(0,0)$, passing through the calculated points, which is narrower than the parent $y=|x|$ graph.

Answer:

The graph of $y=|3x|$ is a horizontally compressed (by factor $\frac{1}{3}$) version of $y=|x|$, with vertex at $(0,0)$, passing through points like $(1,3)$, $(-1,3)$, $(2,6)$, $(-2,6)$, forming a narrower V-shape.