Function

A function relates an input and an output. 1

A function consists of: - a set \(A\) called the domain of the function - a set \(B\) called the codomain of the function - a rule \(f\) that assigns each \(a\in A\) an element \(f(a)\in B\)

There are different ways to think of them: - as rules \(f\) that assigns elements of one set \(X\), elements of another set \(Y\) - as relations \(R\) from \(X\) to \(Y\) where for each \(x \in X\) there is one and only one \(y \in Y\) such that \((x, y)\) is in \(R\). 

If $(x, y)$ is in $R$, we write $y = f(x)$.

  1. https://www.mathsisfun.com/sets/function.html ↩