Question

find g(x), where g(x) is the reflection across the y-axis of f(x) = 3|x + 3| - 10.\
g(x) = 3|x - 3| - 10\
g(x) = 3|x + 3| + 10\
g(x) = -3|x + 3| - 10\
g(x) = -3|x + 3| + 10

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 $f(x)$

$g(x) = f(-x) = 3|-x + 3| - 10$

Step3: Simplify the absolute value term

Since $|-x + 3| = |-(x - 3)| = |x - 3|$, we get $g(x) = 3|x - 3| - 10$.

Answer:

$g(x) = 3|x - 3| - 10$