Campagnolo, Costa, and Moore found connections between discrete complexity classes and analog classes defined on the reals. Building on these ideas Bournez and Hairney found function algebra descriptions of classes of functions defined via real analysis. We develop a general collection of tools which allow us to nicely compare different classes of functions via a notion of "approximation". We apply these general tools to obtain some previous results and prove new ones. Joint work with M. Campagnolo.