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The proper function of an encyclopedia article is, among other things, to describe the usage of technical language in the subject of the article. It is clear to me the following usages for "function" are common:
A function Failed to parse (unknown function "\longarrow"): {\displaystyle f:A\longarrow B}
has a graph, which is a relation on with the functional property. Thus it is "typed" in the sense of my previous post on this Talk Page.
Texts may or may not regard two functions with the same graph but different codomains as the same or different. Thus there are two different meanings of equality for functions and the particular text may not tell you which is being used, and (it appears to me) in many cases it does not even matter, and in other cases it is an important distinction.
Many texts define a function as a functional relation, period.
Some texts assume that "function" means what the rest of us call a "partial function".
The main Wikipedia article on functions should describe all these usages in understandable terms and using easy examples. (For example, is an identity function different from an inclusion function?) I recommend it use "function" for the typed case -- so there are two meanings of equality -- and "functional relation" for the other case. Some authors have recommended that the word "map" be used for the typed case with the stricter meaning of equality (so codomains matter). I think that it is an excellent idea, but it is not common practice.
Arguments for or against particular usages do not belong in Wikipedia. Of course, you can reference arguments in other texts.
