\chapter{Polynomial and rational functions} \section{General rational functions}
Check your understanding
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}
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