If $R = \frac{P}{Q}$ is a rational function, does $f(R) := \deg (P) - \deg (Q)$ have a traditional name/notation?

Question

Suppose $R : C \subseteq \mathbb{R} \rightarrow \mathbb{R}$ is a (univariate) rational function. Write $R=P/Q,$ where $P$ and $Q$ are polynomial functions $\mathbb{R} \rightarrow \mathbb{R}$.

1. Is there a traditional name/notation for the number $f(R)=\deg(P)-\deg(Q)$? (According to wikipedia, the phrase "degree of $R$" is usually understood to mean $\max\{\deg(P), \deg(Q)\}.$)
2. Is there existing terminology to distinguish the cases where $f(R)>0$, $f(R)=0$, and $f(R)<0$? These correspond to different behaviours in the limit as we approach infinity.

Answer 1

On the 18th of November, 2014, KCd said:

In this context you could call it $\deg(R)$. Yes, in other situations the degree of a rational function is defined differently, but this expression is also called the degree of $R$.