[jyounker]

From an algebraic standpoint, the answer is clearly f(x) -> [0, 255].

If you don't have f(n * 0) == n * f(0), then all sorts of weird stuff happens, like:

For f(x) -> [0, 255] then f(0) + f(0) + f(0) = 0 + 0 + 0 = 0 = f(0)

For f(x) -> [0.5/8,7.5/8] then f(0) + f(0) + f(0) = 0.5/8 + 0.5/8 + 0.5/8 = 1.5/8 != f(0)

Choosing the latter means that if you do a calculation on the x side, then you can't expect it to match the calculation on the f(x) side.