Types of functions and relations

Hi,

I seek to understand types of functions and the relation properties that they obey, if there is any at all.

Please add to the list below other types of functions. It seems that designating a "type" of function means that such functions have interesting properties, such as integrals over even and odd functions. Note, I do not include specific groups of functions such as trigometric, exponential, etc, because I seek properties that any function might have.

Composite.
Even and Odd.
Inverse.
Degrees: linear, quadratic, cubic,etc.
Monotonic.
Periodic.
Constant.

Injective.
Surjective.
Bijective.

What is the name of the set whose elements constitute the pairs that the function maps to. for instance, let f: A -> B be a function with elements of the set F <= AxB. What is the formal name of F?

Thanks in advance, Adam.
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