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 $g(x)=4|x|$
b $g(x)=-4|x|$
c $g(x)=\frac{1}{4}|x|$
d $g(x)=-\frac{1}{4}|x|$

Explanation:

Step1: Identify reflection of $g(x)$

The graph of $g(x)$ opens downward, while $f(x)=|x|$ opens upward. This means $g(x)$ is a vertical reflection of $f(x)$, so it has a negative coefficient: $g(x)=-k|x|$ where $k>0$.

Step2: Find vertical scale factor $k$

For $f(x)=|x|$, when $x=1$, $f(1)=1$. For $g(x)$, when $x=1$, $g(1)=-4$. Substitute into $g(x)=-k|x|$:
$-4 = -k|1|$
Solve for $k$: $k=4$

Step3: Write equation for $g(x)$

Substitute $k=4$ into the reflection formula: $g(x)=-4|x|$

Answer:

B. $g(x) = -4|x|$