Mehreren Funktionen in einer Abbildung unterschiedliche Definitionsbereiche geben.

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\documentclass{scrartcl}
\usepackage[ngerman]{babel}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\begin{document}
\begin{center}
\begin{minipage}{\linewidth}
  \centering
  \begin{tikzpicture}[baseline=(current axis.south),scale=0.9]
    \begin{axis}[axis x line=middle, axis y line=middle, xlabel={$y$}, xlabel style={anchor=north}, ylabel={$\Psi(y)$}, ylabel style={anchor=east}, xmin=-1.3, xmax=1.3, ymin=-1.5, ymax=1.5, no marks]
      \addplot[red]coordinates{(-1,-1)(0,-1)};
      \addplot[red]coordinates{(0,1)(1,1)};
      \addplot[red]coordinates{(0,-1)(0,1)};
    \end{axis}
  \end{tikzpicture}\hfill
  \begin{tikzpicture}[baseline=(current axis.south),scale=0.9]
    \begin{axis}[axis x line=middle, axis y line=middle, xlabel={$y$}, xlabel style={anchor=north}, ylabel={$F(x(y),y)$}, ylabel style={anchor=east}, xmin=-1.3, xmax=1.3, ymin=-0.5, ymax=2.5, samples=100, /tikz/smooth, no marks]
      \addplot[red]coordinates{(0,0)(0,1)};
      \addplot[red,domain=0:1]{x^2};
      \addplot[red,domain=-1:0]{1+x^2};
    \end{axis}
  \end{tikzpicture}
  \captionof{figure}{Nicht eindeutige Menge $\Psi(y)$ der unteren Ebene und mögliche Werte der Leader-ZF $F(x(y),y)$}
\end{minipage}
\end{center}
\end{document}
 
 
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