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\begin{frame}
\frametitle{Symmetry}

\begin{block}{}
A function $f$ is called
\begin{itemize}
\item \emph{even} if $f(-x) = f(x)$ for every $x$ in its domain, and
\item \emph{odd} if $f(-x) = -f(x)$ for every $x$ in its domain.
\end{itemize}
\end{block}
\medskip

\begin{minipage}{.49\textwidth}
\begin{center}
\scalebox{.7}{
\begin{tikzpicture}[default]
\def\mfun{{-2 + pow(\x,2) - .08*pow(\x,4)}}
\diagram{-3}{3}{-2}{2}{1}
\diagramannotatez
\draw[cblue,ultra thick] plot[smooth,domain=-3:3,samples=100] (\x,\mfun);
\def\x{2.5}
\node[include=cblue] at (\x,\mfun) {};
\node[anchor=south,yshift=.5mm] at (\x,\mfun) {$(x,f(x))$};
\def\x{-2.5}
\node[include=cblue] at (\x,\mfun) {};
\node[anchor=south,yshift=.5mm] at (\x,\mfun) {$(-x,f(x))$};

\onslide<2->{
\draw[->,red,ultra thick] (.5,1) to[out=-90,in=-80] (-.5,1);
}
\end{tikzpicture}
}\\[.25ex]
an even function
\end{center}
\end{minipage}~
\begin{minipage}{.49\textwidth}
\begin{center}
\scalebox{.7}{
\begin{tikzpicture}[default]
\def\mfun{{2*(\x - .3*pow(\x,3) + .025*pow(\x,5))}}
\diagram{-3}{3}{-2}{2}{1}
\diagramannotatez
\draw[cgreen,ultra thick] plot[smooth,domain=-3:3,samples=100] (\x,\mfun);
\def\x{1.2}
\node[include=cgreen] (a) at (\x,\mfun) {};
\node[anchor=south,yshift=.5mm] at (\x,\mfun) {$(x,f(x))$};
\def\x{-1.2}
\node[include=cgreen] (b) at (\x,\mfun) {};
\node[anchor=north,yshift=-.5mm] at (\x,\mfun) {$(-x,-f(x))$};

\onslide<4->{
\draw[->,red,ultra thick] (.5,1) to[out=-90,in=-80] (-.5,1);
\draw[->,red,ultra thick] (-1,.5) to[out=0,in=10] (-1,-.5);
}
\onslide<5->{
\draw[orange,ultra thick] (a) -- (b);
}
\end{tikzpicture}
}\\[.25ex]
an odd function
\end{center}
\end{minipage}
\pause\medskip

\begin{itemize}
\item even functions are mirrored around the $y$-axis
\pause
\item odd functions are mirrored around the $y$-axis and $x$-axis\\
\pause
(or mirrored through the point $(0,0)$)
\end{itemize}

\end{frame}