\begin{frame}
  \frametitle{Infinite Limits: Definition}
  
  \begin{center}
    \scalebox{.6}{
    \begin{tikzpicture}[default]
      \diagram{-2}{5}{-2}{2.5}{0}
      \diagramannotatez
      \draw[cblue,ultra thick] plot[smooth,domain=-2:1.5,samples=20] function{-(1/((x-2)**2)-3/(x**2 + 3)+0.6)+2};
      \draw[cblue,ultra thick] plot[smooth,domain=2.5:5,samples=20] function{-(1/((x-2)**2)) + 2} node [above] {$f(x)$};
      \node [anchor=south,inner sep=1mm] at (2cm,0cm) {$a$};
      \draw [dashed,cred] (2cm,0cm) -- (2cm,-2cm);
    \end{tikzpicture}
    }
  \end{center}
  
  \begin{block}{}
    Suppose $f(x)$ is defined close to $a$ (but not necessarily $a$ itself).
    Then we write
    \begin{gather*}
      \lim_{x\to a} f(x) = \alert{-\infty}\\[1ex]
      \text{spoken: ``the limit of $f(x)$, as $x$ approaches $a$, is \alert{negative infinity}''}
    \end{gather*}
    if we can make the values of $f(x)$ \alert{arbitrarily large negative}
    by taking $x$ to be sufficiently close to $a$ (but not equal to $a$).
  \end{block}
  \vspace{10cm}
\end{frame}