% Compositions of Functions and Their Graphs
% MATHA 266A Exercise
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{\Large Compositions of Functions and Their Graphs
\footnote{Copyright \copyright 2002, 2004 Winfried Just, Department of Mathematics,
Ohio University. All rights reserved.}}
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\bigskip
Let $f(x) = x^3 - 4x^2 + x - 1$.
\begin{enumerate}
\item Use the \verb$ ezplot $ function
to plot a graph of this function on the interval
$[-2, 4]$.
(Instructions for \verb$ ezplot $ are in the
``Graphing Functions with \textsc{MatLab}'' Exercise.)
\item Let $g(x) = x + 1$. Find formulas for
$g \textsf{\begin{scriptsize} O \end{scriptsize}} f$ and
$f \textsf{\begin{scriptsize} O \end{scriptsize}} g$
(do this by hand).
\item Use \verb$ ezplot $ to plot the graphs of
$f \textsf{\begin{scriptsize} O \end{scriptsize}} g$ and
$g \textsf{\begin{scriptsize} O \end{scriptsize}} f$
on the same plot as the graph of $f$.
\item Correctly label the three functions as ``$f$,''
``$g(f)$'' (for
$g \textsf{\begin{scriptsize} O \end{scriptsize}} f$) and
``$f(g)$'' (for
$f \textsf{\begin{scriptsize} O \end{scriptsize}} g$).
\item Add the title ``\textsc{MatLab} Compositions of Functions'' to your picture.
%%%\item Print your picture and have it ready for possible future submission.
\item If this \textsc{MatLab} exercise is being counted in your grade,
then print this figure for submission.
\end{enumerate}
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