I would like to graph the function $y = \sqrt{x^{2} - 4}/\sqrt{x - 2}$ on the domain from -5 to 30. This function will be Sy = \sqrt{x + 2}$ restricted to the open interval $(2, \infty)$. So, I would like an open circle at (2,0). Now, a horizontal grid line is passing through it, and the graph of the function is passing through it.
I would like a dashed line drawn down to the x-axis from (2,0), and a tick mark there and below it the label "2." I would also like a tick mark below the x-intercept and below it the label "-2."
\documentclass[10pt]{amsart}
\usepackage{tikz}
\usetikzlibrary{calc,angles,positioning,intersections,quotes,decorations.markings}
\usetkzobj{all}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\begin{document}
\begin{tikzpicture}
\begin{axis}[grid=both,
xmax=41,ymax=6,
axis lines=middle,
restrict y to domain=-1.5:6.5,
enlargelimits,
axis line style={shorten >=-0.25cm,shorten <=-0.25cm,latex-latex},
ticklabel style={fill=white}]
\addplot[domain=2:36,mark=none,samples=200] {sqrt(x + 2)} node[fill=white, below]{$y=\frac{x^{2} - 4}{\sqrt{x-2}}$};
\addplot[domain=-2:2,dashed,mark=none,samples=200] {sqrt(x + 2)};
\draw (axis cs:2,2) circle [radius=1.5pt];
\end{axis}
\end{tikzpicture}
\end{document}