Question

f(x) = |6x| - 2; reflection in the y - axis

Explanation:

Step1: Recall reflection rule

When reflecting a function $y = f(x)$ in the $y$-axis, we replace $x$ with $-x$.

Step2: Apply the rule

Given $f(x)=\vert6x\vert - 2$, after reflection in the $y$-axis, we get $f(-x)=\vert6(-x)\vert - 2=\vert - 6x\vert - 2$. Since $\vert - 6x\vert=\vert6x\vert$, the new function is $y=\vert6x\vert - 2$.

Answer:

$y = \vert6x\vert - 2$