In mathematics, a surjective function (also known as surjection, or onto function) is a function f that maps an element x to every element y; that is, for every y, there is an x such that f(x) = y. In other words, every element of the function's codomain is the image of at least one element of its domain. It is not required that x be unique; the function f may map one or more elements of X to the same element of Y. * A non-injective surjective function (surjection, not a bijection) * An injective surjective function (bijection) * An injective non-surjective function (injection, not a bijection)