\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}