Question

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

Explanation:

Step1: Recall reflection over y - axis rule

The rule for reflecting a function \(y = f(x)\) across the \(y\) - axis is \(y=f(-x)\).

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

Given \(f(x)=\vert x\vert\), to find the reflection across the \(y\) - axis, we substitute \(-x\) for \(x\) in \(f(x)\). So \(g(x)=f(-x)=\vert - x\vert\).
Since \(\vert - x\vert=\vert x\vert\) for all real numbers \(x\), and we need to write it in the form \(a\vert x - h\vert + k\). Here, \(a = 1\), \(h = 0\), and \(k = 0\) because \(\vert x\vert=1\times\vert x - 0\vert+0\).

Answer:

\(1\vert x - 0\vert+0\) (or simply \(\vert x\vert\) as \(1\vert x - 0\vert+0\) simplifies to \(\vert x\vert\))