Let $F$ be a field. What is the best notation (in an undergraduate or graduate abstract algebra class) for a generic element of the univariate polynomial ring $F[x]$?
The most common notation seems to be $f(x)$. It seems strongly to me that $f$ (or any other single letter) is to be preferred: it emphasizes that elements of $F[x]$ are well-defined objects, without reference to plugging in anything for $x$, and that if you see $f(a)$, this always indicates the evaluation homomorphism obtained by replacing $x$ with $a$.
There is no logical conflict here, because the tautological evaluation homomorphism $F[x] \rightarrow F[x]$ sending $x$ to $x$ is just the identity. Nevertheless, I cannot help but feel that writing $f(x)$ sends the wrong message.
Nevertheless, judging from a skimming of the algebra textbooks on my shelf, I seem to be in the minority. Is there reason to prefer writing $f(x)$?