Question

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) = input box 0 submit button

Explanation:

Step1: Recall reflection rule

Reflecting a function \( y = f(x) \) across the \( x \)-axis transforms it to \( y=-f(x) \).

Step2: Apply to \( f(x)=\vert x\vert \)

Given \( f(x)=\vert x\vert \), its reflection \( g(x) \) across the \( x \)-axis is \( g(x)=-f(x)=-\vert x\vert \). In the form \( a\vert x - h\vert + k \), we have \( a = - 1 \), \( h = 0 \), \( k = 0 \), so \( g(x)=-1\vert x - 0\vert+0=-\vert x\vert \).

Answer:

\( g(x)=-\vert x\vert \) (or in the required form \( -1\vert x - 0\vert + 0 \))