Question

ing at the parent function of $f(x)=|x|$ how would the graph of $g(x)=3f(x)$ be different? graph using the ing tools.

Explanation:

Step1: Define the transformed function

Substitute $f(x)=|x|$ into $g(x)$:
$g(x)=3|x|$

Step2: Compare vertical outputs

For any $x$, $g(x)$ is 3 times $f(x)$:
For $x=1$: $f(1)=1$, $g(1)=3$; for $x=-2$: $f(-2)=2$, $g(-2)=6$

Step3: Describe transformation type

This is a vertical stretch by factor 3.

Answer:

The graph of $g(x)=3f(x)$ is a vertical stretch of the parent function $f(x)=|x|$ by a factor of 3: every $y$-value of the parent function is multiplied by 3, making the V-shape narrower and steeper, while still having its vertex at the origin $(0,0)$. For example, when $x=2$, $f(2)=2$ and $g(2)=6$; when $x=-3$, $f(-3)=3$ and $g(-3)=9$.