# What is the range of the function f(x) = 4 /(x -3)?

The domain is ${D}_{f} = R - \left\{3\right\}$ and the range is
$y = f \left(x\right) = \frac{4}{x - 3}$
$x - 3 = \frac{4}{y}$
$x = 3 + \frac{4}{y}$ (For this to have a meaning $y \ne 0$)
Hence the range is ${R}_{f} = R - \left\{0\right\}$