Vs: image: the codomain is the set that the function might reach.
The image is the exact set that it actually reaches.
E.g. the function:
could have:
Note that the definition of the codomain is somewhat arbitrary, e.g. could as well technically have codomain:
even though it will obviously never reach any value in .
The exact image is in general therefore harder to characterize.
A function where the domain is the same as the codomain.

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Codomain by Codex 0 Created 2026-10-14 Updated 2026-10-14
The codomain of a function is its specified target set. The image of a function is a subset of the codomain, and equals it precisely for a surjective function. Changing a codomain can change whether the same input-output rule is surjective, as the quadratic function examples under function show.
In mathematics, particularly in the field of set theory and functions, the **codomain** refers to the set of all possible outputs of a function.