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\begin{document}
\begin{center}

\Huge{Polynomials}
\end{center}



\noindent

\begin{enumerate}
\item Use your own words to define what a polynomial function is.
\vskip 1in
\item Compare your definition with that on page 250 of Stewart's textbook.  Are they consistent with each other? 
\vskip 1in
\item What other words did Stewart define in the definition on page 250?
\vskip 1in
\item For each of the expressions below, determine if it is a polynomials and \emph{if it is}, determine the degree:

\vskip .2in

\begin{tabular*}{5in}{l|l|l}
expression & polynomial?  & degree\\
		&(yes/no) &(if applicable) \\
&&\\
$117x^4+6x^{12}+x$&&\\ \hline
&&\\
$2^x-5x^2$&&\\ \hline
&&\\
$\sqrt{5}x^2-\pi$ && \\ \hline
&&\\
$7x^8-4.56x^4-7x^8+x^2$&&\\ \hline
&&\\
$3$&&\\ \hline
\end{tabular*}

\vfill
\noindent Consider checking your answers with a group near by, or consult Stewart's text on page 250.

\newpage
We have already spent a few days on first degree and second degree polynomials.  We now turn to higher order polynomials.

\item Fill out as much of the following table as necessary to sketch a graph of the function $$f(x)=x^3.$$ 

\begin{tabular*}{1in}{l|l}
$x$ & $f(x)=x^3$\\
-1 & \\
\hline
&\\
$\frac{-3}{4}$ &\\
\hline
&\\
$\frac{-1}{2}$ &\\
\hline
&\\
$\frac{-1}{4}$ &\\
\hline
&\\
0&\\
\hline
&\\
$\frac{1}{3}$&\\
\hline
&\\
$\frac{1}{3}$ &\\
\hline
&\\
1 &\\
\end{tabular*}



\vskip -3in \hskip 1.5in \includegraphics[height=2.3in]{Blank1}

\vskip 1in

\item Fill out as much of the following table as necessary to sketch a graph of the function $$g(x)=x^5.$$ 

\begin{tabular*}{1in}{l|l}
$x$ & $g(x)=x^5$\\
-1 & \\
\hline
&\\
$\frac{-3}{4}$ &\\
\hline
&\\
$\frac{-1}{2}$ &\\
\hline
&\\
$\frac{-1}{4}$ &\\
\hline
&\\
0&\\
\hline
&\\
$\frac{1}{3}$&\\
\hline
&\\
$\frac{1}{3}$ &\\
\hline
&\\
1 &\\
\end{tabular*}



\vskip -3in \hskip 1.5in \includegraphics[height=2.3in]{Blank1}

\newpage
\item Do you see any similarities between the graphs of $x^3$ and $x^5$? What do you think the graph of $h(x)=x^7$ would look like?
\vskip 1in

\item Consider the ``end behavior" of polynomials like $x^3$, $x^5$, and $x^7$.  That is, what happens when $x$ ``gets very large in the  positive direction" ($x\rightarrow \infty$) and what happens when $x$ ``gets very large in the negative direction" ($x\rightarrow -\infty$)?  
\vskip 1in

\item Which of the following could be a graph of $x^{11}$? Why or why not?

\hspace{-.5in}\includegraphics[height=2in]{x^6}\hspace{.4in}\includegraphics[height=2in]{x^11}
\vfill

\item Use your observations of ``end behavior" and identify which (if any) of the following could be the graph of an odd degree polynomial? (Not necessarily of the form $x^{n}$ but like the polynomials you looked at on page 1)?

\hspace{-.5in}\includegraphics[height=2in]{x^5}\hspace{.4in}\includegraphics[height=2in]{x^3}

\newpage
\item Let $f(x)=x^3$. Use question 5 and \S2.4 (what was that over again?) to graph:

$m(x)=-f(x+1)=-(x+1)^3$ \hspace{.4in}and\hspace{.4in} $n(x)=-f(x)-1=-x^3-1$

\vskip .2in

\hspace{-.75in} \includegraphics[height=1.75in]{Blank1} \hspace{.25in} \includegraphics[height=1.75in]{Blank1} 



\end{enumerate}

\end{document}
