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Is the term “function” well defined?

I have discovered that even experienced teachers do not notice that the word “function” means two different things in different contexts, sometimes it means the “dependent variable f(x)” (like when we say “increasing function”) and sometimes it means “an operation f(  )” (like when  we say “define the function as f(x)=x+2”). Some students, particularly, those sensitive to language get thoroughly confused and begin to think they could never grasp maths.

Even though Wikipedia is not the final authority on all things, it does give a nice history of the concept:

http://en.wikipedia.org/wiki/History_of_the_function_concept

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