\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}