Final answer:
The function g(x) is the reflection of f(x) = 9|x - 3| + 6 across the y-axis and is found by replacing x with -x in f(x), which results in g(x) = 9|3 - x| + 6.
Step-by-step explanation:
The question involves finding the function g(x) which is the reflection of the given function f(x) = 9|x - 3| + 6 across the y-axis. To reflect a function across the y-axis, you replace x with -x in the function. The correct function g(x) would, therefore, have each x replaced with -x, resulting in g(x) = 9|-x - 3| + 6. Simplifying the absolute value expression gives g(x) = 9|3 - x| + 6, which matches option a.
To find the reflection across the y-axis of a function, we replace every occurrence of x with -x in the original function. In this case, the original function is f(x) = 9|x - 3| + 6. So, replacing x with -x gives us g(x) = 9|-x - 3| + 6. Simplifying further, we get g(x) = 9|-(x + 3)| + 6. Lastly, we can simplify this to g(x) = 9|3 - x| + 6, which is option a.