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\begin{frame}
  \frametitle{Rational Functions}
  
  \vspace{-1ex}
  \begin{block}{}
    A \emph{rational function} $f$ is ratio of two polynomials:
    \begin{talign}
      f(x) = \frac{P(x)}{Q(x)} &&\text{where $P$ and $Q$ are polynomials}
    \end{talign}
  \end{block}
  \medskip\pause
  \begin{itemize}
    \item the domain of $\frac{P(x)}{Q(x)}$ is $\{\,x \mid Q(x) \ne 0\,\}$
  \end{itemize}

  \pause
  \begin{center}
  \begin{minipage}{.4\textwidth}
  \scalebox{.6}{
  \begin{tikzpicture}[default,baseline=1cm]
    \diagram{-3}{3}{-3}{3}{1}
    \diagramannotatez
    \diagramannotatex{-1,1}
    \diagramannotatey{-1,1}
    \begin{scope}[ultra thick]
    \draw[cblue] plot[smooth,domain=0.33:3,samples=100] (\x,{1/\x});
    \draw[cblue] plot[smooth,domain=-3:-0.33,samples=100] (\x,{1/\x});
  \end{scope}
  \end{tikzpicture}
  }\\\smallskip
  \centerline{$f(x) = \frac{1}{x}$}
  \end{minipage}\hspace{1cm}
  \begin{minipage}{.4\textwidth}
  \scalebox{.465}{
  \begin{tikzpicture}[default,baseline=0ex]
    \diagram{-4}{4}{-3}{5}{1}
    \diagramannotatez
    \diagramannotatex{-1,1}
    \diagramannotatey{-1,1}
    \draw[cblue,ultra thick] plot[smooth,domain=-1.83:1.83,samples=20] (\x,{(2*pow(\x,4)-pow(\x,2)+1) / (10*pow(\x,2) - 40))});
    \draw[cblue,ultra thick] plot[smooth,domain=2.21:3.95,samples=20] (\x,{(2*pow(\x,4)-pow(\x,2)+1) / (10*pow(\x,2) - 40))});
    \draw[cblue,ultra thick] plot[smooth,domain=-3.95:-2.21,samples=20] (\x,{(2*pow(\x,4)-pow(\x,2)+1) / (10*pow(\x,2) - 40))});
  \end{tikzpicture}
  }\\\smallskip
  \centerline{$f(x) = \frac{2x^4 - x^2 +1}{10x^2 - 40}$}
  \end{minipage}
  \end{center}
\end{frame}