The image of a function is not to be confused with the codomain, which is the type of output that the function produces\. For example, the function $~$f(x)\=1$~$ that always returns $~$1$~$ has image $~$\\{1\\}$~$, even though its codomain is the set of all numbers\.

Okay now I'm also confused. (Eric Rogstad)

Why don't we just say its codomain is {1}?