\chapter{Polynomial and rational functions}
\section{Polynomial functions}
Answer the questions in your own words.
\begin{enumerate}
\item Explain why \(f(x) = 3x^4-5x^2+x\sqrt{5}+1\) a polynomial, but
\(g(x) = 3x^4-5x^2+5\sqrt{x}+1\) is not.
\item
What is the degree of \(f(x)=\pi^3 x+5\)?
\item
What is the constant term of the polynomial \(p(x)=x^4-x^2+x\)?
\item
What is the coefficient of \(x\) for the polynomial \(\displaystyle g(x)=\frac{\pi x^5}{3}
-\frac{\pi x^2}{6}+\frac{2\pi x}{3}\)?
\item
What is the maximum number of turning points that a polynomial of degree 19
could have?
\item
What is the maximum number of \(x\)-intercepts that a polynomial of degree 15 could have?
\item
Suppose that \(x_1\) is a zero of a polynomial. That means that \( (x_1,0) \) is an \(x\)-intercept
for the polynomial. What else do you need to know to
find out if the \(x\)-intercept is of type bouncing or crossing?
\item Both the degree and the sign of the leading coefficient determine the end behavior of
a polynomial. Can you explain how that works?
\end{enumerate}