\begin{frame} \frametitle{Infinite Limits: Vertical Asymptotes} \begin{block}{} The line $x = a$ is a \emph{vertical asymptote} of a function $f$ if at least one of the following statements is true: \begin{talign} \lim_{x\to a} f(x) &= \infty & \lim_{x\to a^-} f(x) &= \infty & \lim_{x\to a^+} f(x) &= \infty\\ \lim_{x\to a} f(x) &= -\infty & \lim_{x\to a^-} f(x) &= -\infty & \lim_{x\to a^+} f(x) &= -\infty \end{talign} \end{block} \medskip \begin{center} \scalebox{.6}{ \begin{tikzpicture}[default] \diagram{-2}{5}{-.5}{4}{0} \diagramannotatez \draw[cblue,ultra thick] plot[smooth,domain=-2:1.5,samples=20] function{1/((x-2)**2)-3/(x**2 + 2)+0.7}; \draw[cblue,ultra thick] plot[smooth,domain=2.5:5,samples=20] function{1/((x-2)**2)} node [above] {$f(x)$}; \node [anchor=north,inner sep=1mm] at (2cm,0cm) {$a$}; \draw [dashed,cred] (2cm,0cm) -- (2cm,4cm); \end{tikzpicture} } \end{center} \end{frame}