Question

function g can be thought of as a scaled version of $f(x)=|x|$.
graph of f(x) = |x| (blue solid line) and g(x) (red dashed line) on a coordinate plane
what is the equation for g(x)?
choose 1 answer:
a $g(x)=2|x|$
b $g(x)=-2|x|$
c $g(x)=\frac{1}{2}|x|$
d $g(x)=-\frac{1}{2}|x|$

Explanation:

Step1: Identify parent function

$f(x) = |x|$

Step2: Analyze vertical scaling

For $f(x)=|x|$, at $x=2$, $f(2)=2$. For $g(x)$, at $x=2$, $g(2)=1$. Find scaling factor $a$: $g(x)=a|x|$, so $1=a\times2$, $a=\frac{1}{2}$.

Step3: Check direction (no reflection)

$g(x)$ has same sign as $f(x)$, so no negative factor.

Answer:

C. $g(x) = \frac{1}{2}|x|$