What is a function in mathematics?

A function $f: X \to Y$ is a rule that assigns to each element $x$ in a non-empty set $X$ (called the domain or independent variable) exactly one element $y$ in another non-empty set $Y$ (called the co-domain or dependent variable). This relationship is expressed as $y = f(x)$. Essentially, for every input $x$, there is a unique output $y$.