Consider the function f: . 

For every x₁, x₂A if  x₁ ? x₂ implies

f(x₁) ? f(x₂)

then the function f is called one-to-one (or injective), so the correct answer is A.

Although the range and the image of a function are two concepts that need to be distinguished, we still know that they are closely related. The image is always a subset of the range. Yet, there are functions for which the range and the image sets are exactly the same. Thus, given a function f : if the image is equal to the range, i.e. f (A)=B the function f  is called surjective (onto). Equivalently, for every element b of the set B if there can be found an element a of A such that f (a)=b, then f  is called onto.

If a function which is both one-to-one and onto is called a bijection.

Constant function and identity function are the concepts related to types of functions.

A function assigning each element from its domain a single element in its range is called a constant function.

Given A ?, a function defined on the set A and assigning every element of A to itself is called the identity function.