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Band2/Grafiken/B2_5.tikz

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+\begin{tikzpicture}
+[line cap=round,line join=round,x=1cm,y=1cm]
+\tikzset{
+        every pin/.style={fill=yellow!50!white,rectangle,rounded corners=3pt,font=\tiny},
+        small dot/.style={fill=black,circle,scale=0.3},}
+\begin{axis}[
+x=2cm,y=2cm,
+axis lines=middle,
+axis line style = {-latex},
+xmin=-1,
+xmax=3,
+ymin=-0.5,
+ymax=2,
+ytick={1,2},
+yticklabels={1,2},
+xtick=\empty,
+xlabel=$x$,
+ylabel=$y$,
+extra x ticks={0.5},
+    extra x tick style={
+        tick label style={anchor=north}},
+    extra x tick labels={$\frac{1}{2}$},
+enlargelimits = true,
+]
+
+
+
+\draw [thick, dashed] (axis cs: -0.05,1) -- (axis cs: 0.5,1);
+\draw [thick, dashed] (axis cs: 0.5,-0.05) -- (axis cs: 0.5,1);
+
+
+\addplot[domain=-1:0.5, blue, line width=1,samples=2000] {((x^2)-(1/4))/(x-(1/2)};
+\addplot[color=blue!80!black, only marks, style={mark=*, fill=white}] coordinates {(0.5,1)};
+\addplot[domain=0.51:1.5, blue, line width=1,samples=2000] {((x^2)-(1/4))/(x-(1/2)};
+
+\addplot[color=blue!80!black, only marks, style={mark=*}] coordinates {(0.5,2)};
+
+\draw [thick, dashed] (axis cs: -0.05,2) -- (axis cs: 0.5,2);
+\draw [thick, dashed] (axis cs: 0.5,1) -- (axis cs: 0.5,2);
+
+
+
+\scriptsize{ \node () at (axis cs:2.4,1.8) {$\displaystyle y=\left\{ \begin{array}{rl}
+\frac{x^2-\frac{1}{4}}{x-\frac{1}{2}} & \text{für}\; x \neq \frac{1}{2}\\ \\
+2 & \text{für}\; x = \frac{1}{2}\\
+\end{array}
+\right .$};}
+
+% \draw[] (axis cs:1.3, 0.1) -- (axis cs:1.3, -0.1);
+% \node () at (axis cs:1.3,-0.25) {$x_0$};
+
+% \draw[] (axis cs:1.14,-0.05) -- (axis cs:1.14, 0.05);
+% \node () at (axis cs:0.33,-0.45) {$\frac{1}{\pi}$};
+
+\end{axis}
+
+
+\end{tikzpicture}