In mathematics, and more specifically in naïve set theory, the range of a function refers to either the codomain or the image of the function, depending upon usage. Modern usage almost always uses range to mean image. In mathematics, and more specifically in naïve set theory, the range of a function refers to either the codomain or the image of the function, depending upon usage. Modern usage almost always uses range to mean image. The codomain of a function is some arbitrary super-set of image. In real analysis, it is the real numbers. In complex analysis, it is the complex numbers.