\begin{frame}
  \frametitle{Infinite Limits: Vertical Asymptotes}

  \begin{exampleblock}{}
    What are the vertical asymptotes of 
    \begin{talign}
      f(x) = \frac{2x}{x-3} \;\text{ ?}
    \end{talign}
  \end{exampleblock}
  \pause\smallskip
  
  \begin{center}
    \scalebox{.7}{
    \begin{tikzpicture}[default,baseline=-1ex]
      \diagram{-1}{5}{-2}{2}{0}
      \diagramannotatez
      \diagramannotatex{1,2,3,4}
      \node at (0,1cm) [anchor=east,inner sep=1mm] {5};
      \draw[cblue,ultra thick] plot[smooth,domain=-1:2.5,samples=20] function{(2*x)/(x-3)/5};
      \draw[cblue,ultra thick] plot[smooth,domain=3.6:5,samples=20] function{(2*x)/(x-3)/5} node [below] {$f(x)$};
      \draw [dashed,cred] (3cm,-2cm) -- (3cm,2cm);
    \end{tikzpicture}
    }
  \end{center}
  
  The function has the vertical asymptote $x = 3$:
  \begin{talign}
    \lim_{x \to 3^-} f(x) = -\infty 
  \end{talign}
\end{frame}