Question

function g can be thought of as a scaled version of $f(x)=|x|$.
what is the equation for $g(x)$?
choose 1 answer:
a $g(x)=-\frac{4}{3}|x|$
b $g(x)=\frac{4}{3}|x|$
c $g(x)=-\frac{3}{4}|x|$
d $g(x)=\frac{3}{4}|x|$

Explanation:

Step1: Identify scaling factor logic

A scaled version of $f(x)=|x|$ has form $g(x)=k|x|$, where $k$ is the vertical scale factor. We use a point on $g(x)$ to find $k$.

Step2: Pick point on $g(x)$

From the graph, when $x=4$, $g(x)=3$. Substitute into $g(x)=k|x|$:
$3 = k|4|$

Step3: Solve for $k$

$3 = 4k$
$k = \frac{3}{4}$
Since $g(x)$ opens upward (same direction as $f(x)$), $k$ is positive.

Step4: Write $g(x)$ equation

Substitute $k=\frac{3}{4}$ into $g(x)=k|x|$.

Answer:

D. $g(x) = \frac{3}{4}|x|$