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

  \begin{exampleblock}{}
    What are the vertical asymptotes of 
    \begin{talign}
      f(x) = \frac{x^2 + 2x -3}{x-1} \;\text{ ?}
    \end{talign}
  \end{exampleblock}
  \pause\smallskip
  
  \begin{center}
    \scalebox{.6}{
    \begin{tikzpicture}[default,baseline=-1ex,yscale=.8]
      \diagram{-3}{3}{-1}{6}{0}
      \diagramannotatez
      \diagramannotatex{1,2}
      \diagramannotatey{1,2,3,4,5}
      \draw[cblue,ultra thick] plot[smooth,domain=-3:3,samples=20] function{(x**2 + 2*x -3)/(x-1)} node [above] {$f(x)$};
      \node[exclude=cblue] at (1,4) {};
    \end{tikzpicture}
    }
  \end{center}
  
  The function has no vertical asymptotes:
  \begin{talign}
    \frac{x^2 + 2x -3}{x-1} = (x+3) \text{ for $x \ne 1$} 
  \end{talign}
\end{frame}