\chapter{Polynomial and rational functions}
\section{General rational functions}
Answer the questions in your own words.
\begin{enumerate}
\item Explain how to find vertical asymptotes and holes for the rational
function \(\displaystyle f(x)=\frac{p(x)}{q(x)}\).
\item Explain how to find horizontal asymptotes for the rational
function \(\displaystyle f(x)=\frac{p(x)}{q(x)}\).
\item Suppose that \(\displaystyle f(x)=\frac{x^2+1}{q(x)}\), and \(q(2)=0\). Could \(x=2\) be a
hole for \(f(x)\)?
\item Suppose now that \(\displaystyle f(x)=\frac{p(x)}{x-3}\), and \(p(3)=0\). Could \(x=3\) be a
vertical asymptote for \(f(x)\)?
\item Suppose that \(\displaystyle f(x)=\frac{p(x)}{(x-3)^2}\), and \(p(3)=0\). Is \(x=3\) a hole
or a vertical asymptote?
\end{enumerate}