When a function is reflected across the y-axis, all the x-values become their opposites. This means that if we have a point (x,y) on the original function f(x), the corresponding point on the reflected function g(x) would be (-x,y).
Using this idea, we can find the equation of g(x) by starting with the equation of f(x) and replacing x with -x:
f(x) = 4x - 8
g(x) = f(-x) (reflecting f(x) across the y-axis)
= 4(-x) - 8
= -4x - 8
Therefore, the equation of the reflected function g(x) is g(x) = -4x - 8.