Question

find g(x), where g(x) is the reflection across the y - axis of f(x) = - 6|x - 9| - 9.
options:

1. g(x) = - 6|x - 9| + 9
2. g(x) = 6|x - 9| - 9
3. g(x) = 6|x + 9| + 9
4. g(x) = - 6|x + 9| - 9

Explanation:

Step1: Apply 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 $f(x)$

$$g(x) = f(-x) = -6|(-x) - 9| - 9$$

Step3: Simplify the absolute value term

$$g(x) = -6| - (x + 9)| - 9$$
Since $| -a | = |a|$, we get:
$$g(x) = -6|x + 9| - 9$$

Answer:

$g(x) = -6|x + 9| - 9$