On the Number of Distinct Values of a Class of Functions with Finite Domain

By relating the number of images of a function with finite domain to a certain parameter, we obtain both an upper and lower bound for the image set. Even though the arguments are elementary, the bounds are, in some sense, best possible. These bounds are then applied in several contexts. In particular, we obtain the first non-trivial upper bound for the image set of a planar function over a finite field.