is there a function to figure out all functions

Question

I am trying to figure out whether it is possible to use one function to figure out all functions. 

Answer 1

Sounds similar to TOE, the Theory Of Everything, a physics equation which explains everything

Maybe a function which in its generality encompasses all other functions as special cases.

Newtonian physics is a special case of Einstein's Theory of Relativity.

f(x) = a + bx + cx^2 + dx^3 + ... sx^n + ... zzzx^n+m

encompasses all polynomial functions with integer exponents

add in trig functions, exponential functions, log functions, step functions, into one big function would be sort of like refinancing all those nagging little bills into one huge back breaking debt.