Question

find g(x), where g(x) is the reflection across the y-axis of f(x) = 3|x - 8| + 9. write your answer in the form a|x - h| + k, where a, h, and k are integers. g(x) = |0|

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 $-x$ into $f(x)$

$g(x) = f(-x) = 3|-x - 8| + 9$

Step3: Simplify the absolute value term

Factor out $-1$ inside the absolute value: $|-x - 8| = |-(x + 8)| = |x + 8| = |x - (-8)|$

Step4: Rewrite in required form

Substitute back to get $g(x) = 3|x - (-8)| + 9$

Answer:

$3|x + 8| + 9$