Find g(x), where g(x) is the reflection across the x-axis of f(x)=2|x+4|–4.

To find the reflection of the function f(x) = 2|x+4| - 4 across the x-axis, you simply need to change the sign of the entire function. This is because reflecting a function across the x-axis means that the y-values of the function are negated.

So, the reflection of f(x) across the x-axis, which we'll call g(x), is:

g(x) = -f(x) = -(2|x+4| - 4) = -2|x+4| + 4

So, g(x) = -2|x+4| + 4 is the reflection of the function f(x) = 2|x+4| - 4 across the x-axis.