Question

find g(x), where g(x) is the reflection across the y-axis of f(x) = 2|x - 6| - 10. write your answer in the form a|x - h| + k, where a, h, and k are integers. g(x) = \boxed{}

Explanation:

Step1: Recall y-axis reflection rule

To reflect a function $f(x)$ across the y-axis, replace $x$ with $-x$ in the function.

Step2: Substitute $x=-x$ into $f(x)$

$g(x) = 2|-x - 6| - 10$

Step3: Rewrite the absolute value term

Factor out $-1$ inside the absolute value: $|-x - 6| = |-(x + 6)| = |x + 6| = |x - (-6)|$, since $|ab|=|a||b|$ and $|-1|=1$.
Substitute back: $g(x) = 2|x - (-6)| - 10$

Answer:

$2|x + 6| - 10$