find g(x), where g(x) is the reflection across the x - axis of f(x) = |x|. write your answer in the form a|x…

find g(x), where g(x) is the reflection across the x - axis of f(x) = |x|. write your answer in the form a|x - h| + k, where a, h, and k are integers. g(x) =

find g(x), where g(x) is the reflection across the x - axis of f(x) = |x|. write your answer in the form a|x - h| + k, where a, h, and k are integers. g(x) =

Answer

Explanation:

Step1: Recall reflection rule

When a function $y = f(x)$ is reflected across the $x - axis$, the transformation is $y=-f(x)$.

Step2: Apply to given function

Given $f(x)=|x|$, then $g(x)=-|x|$. In the form $a|x - h|+k$, we have $a=- 1$, $h = 0$, $k = 0$. So $g(x)=-1|x - 0|+0$.

Answer:

$-|x|$