\subsection{11\_1 Der Betrag in $\mathbb R$}

\begin{tabbing}
\tabumg
\>wird für $x\in\mathbb R$ mit $|x|$ bezeichnet\\
\>ist definiert durch $
\left| x \right| = \left\{ {\begin{array}{*{20}c}
   {x\text{   falls  }x \ge 0}  \\
   { - x\text{   falls  }x < 0}  \\
\end{array}} \right.$\\
\\
Veranschaulichungen:\\
\>auf der Zahlengeraden:

\end{tabbing}
%\vspace{-10mm}
\begin{figure}[h]
\begin{center}
%\includegraphics{11_1_1}


\begin{tikzpicture}[scale=1.2]

    \draw [thick](-2.5,0) -- (3.5,0);
    \draw [thick, style=dotted](3.5,0) -- (4,0);
    \draw [thick, style=dotted](-3,0) -- (-2.5,0);

    \foreach \x/\xtext in {-2/x_2,0,1, 3/x_1}
      \draw[xshift=\x cm, thick] (0pt,1pt) -- (0pt,-1pt) node[below,fill=white]
            {$\xtext$};

    \draw[snake=brace, mirror snake, color=blue] (-2,-0.4) -- (0,-0.4) node[midway,sloped,below] {$|x_1|$};
    \draw[snake=brace, mirror snake, color=red] (0,-0.4) -- (3,-0.4) node[midway,sloped,below] {$|x_2|$};

\end{tikzpicture}
  \end{center}
\end{figure}
\vspace{-15mm}
\begin{tabbing}
\tabumg
\>\>\>$x$ ist der Abstand von $x$ vom Nullpunkt\\
\\
\>durch den Funktionsgraphen:
\end{tabbing}
\vspace{-10mm}
\begin{figure}[h]
\begin{center}
\includegraphics{11_1_2}
  \end{center}
\end{figure}
\vspace{-10mm}
\begin{tabbing}
\tabumg
Rechenregeln:\\
\>$|x\cdot y|=xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx$
\end{tabbing}
