# Domain, Codomain, Range, Image (mathematics) We can define a function as: $f: X \rightarrow Y$ We can the define these terms as follows: * **[Domain](https://en.wikipedia.org/wiki/Domain_of_a_function)**: The set of departure of a function. It is the set into which all of the input of the function is constrained to fall. It is $X$, in red below. * **[Codomain](https://en.wikipedia.org/wiki/Codomain)**: The set of destination of a function. It is the set into which all of the output of a function is constrained to fall. It is $Y$, in blue below. * **[Image](https://en.wikipedia.org/wiki/Image_(mathematics))**: The image of a function is the set of all output values it may produce. It is $f(X)$, the yellow oval below. It is also known as the **range**.