Definition:Rational Function/Real

Definition
Let $P: \R \to \R$ and $Q: \R \to \R$ be polynomial functions on the set of real numbers.

Let $S$ be the set $\R$ from which all the roots of $Q$ have been removed.

That is:
 * $S = \R \setminus \set {x \in \R: \map Q x = 0}$.

Then the equation $y = \dfrac {\map P x} {\map Q x}$ defines a function from $S$ to $\R$.

Such a function is known as a rational function.