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\begin{frame}
\frametitle{Continuity: Examples}

\begin{center}
\scalebox{.8}{
\begin{tikzpicture}[default]
\diagram{-.5}{9}{-.5}{3.2}{1}
\diagramannotatez
\diagramannotatex{1,2,3,4,5,6,7,8}
\diagramannotatey{1,2}
\draw[cred] (-.5,0) to[out=51,in=180] (3,3);
\draw[cred] (3,2) to[out=-45,in=180] (5,1);
\draw[cred] (5,1) to[out=0,in=150] (9,3);

\node[exclude={cred}] at (1,2) {};
\node[include={cred}] at (3,2) {};
\node[exclude={cred}] at (3,3) {};
\node[exclude={cred}] at (5,1) {};
\node[include={cred}] at (5,2.5) {};
\end{tikzpicture}
}
\end{center}

Where is this graph continuous/discontinuous?
\begin{itemize}
\pause
\item discontinuous at $x = 1$ since $f(1)$ is not defined
\pause
\item discontinuous at $x = 3$ since $\lim_{x\to 3} f(x)$ does not exist
\pause
\item discontinuous at $x = 5$ since $\lim_{x\to 5} f(x) \ne f(5)$
\end{itemize}
\pause
Everywhere else it is continuous.
\end{frame}