\chapter{Polynomial and rational functions}
\section{Fractional linear functions}
Answer the questions in your own words.
\begin{enumerate}
\item What is a rational function?
\item Explain why \(\displaystyle \frac{2+\sqrt{3}}{2+\sqrt{5}}\) is not a rational number,
\(\displaystyle \frac{x+\sqrt{3}}{x+\sqrt{5}}\) is a rational function, and \( \displaystyle
\frac{2+\sqrt{x}}{2+\sqrt{5}}\) is not a rational function.
\item What are the asymptotes of the reciprocal function \(f(x)=1/x\)?
\item What are domain and range for the reciprocal function \(f(x)=1/x\)?
\item Does the reciprocal function \(f(x)=1/x\) have any \(x\)- or \(y\)- intercepts?
\item The function \(g(x)\) is obtained by shifting the reciprocal function \(f(x)=1/x\)
right by \(3\) and up by \(5\). What are the asymptotes, domain and range for \(g(x)\)?
\item Suppose you are given a rational function such as \(\displaystyle
f(x)=\frac{ax+b}{x-c}\). How can you find the transformations that will take you from
the parent function \(1/x\) to \(f(x)\)?
\end{enumerate}