To reflect a function across the x-axis, you need to transform the function by multiplying it by -1. This changes the sign of all the output values for the function.
Given the function:
f(x) = 508x
The reflection across the x-axis can be represented as:
g(x) = -f(x)
Substituting in the original function:
g(x) = -508x
Thus, the function that represents the reflection of f(x) = 508x across the x-axis is:
g(x) = -508x
This transformation effectively inverts the graph of the original function, ensuring that every point (x, y) on the graph of f(x) corresponds to the point (x, -y) on the graph of g(x).