In mathematics, and more specifically in naïve set theory, the range of a function refers to the codomain of the function, though depending upon usage it can sometimes refer to the 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.
The image of a function is the set of all outputs of the function. The image is always a subset of the codomain.