A "Function" takes elements from one collection (domain of a function) and assigns to it, or returns, an element from another collection (co-domain of a function, image of a function, range of a function).

Functions appear everywhere in mathematics. Examples include:

• Simple polynomials: $f(x)~=~x^3-2x+5$
• Exponential functions: $f(x)~=~e^x$
However, functions can be much more complex, not described by a single formula, and functions don't necessarily work only and/or entirely on the real numbers. Functions in general carry elements of one set to another set, not necessarily the same.
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