\begin{tikzpicture}[scale=2]
\definecolor{mycolor1}{rgb}{0.15, 0.47, 0.70}

%\draw[->] (-1.5,-1.5) -- (2,-1.5) node[right] {$x$};
%\draw[->] (-1.5,-2.5) -- (-1.5,0.8) node[left]{\footnotesize{$y=f(x)$}};
%\clip[draw](-1.5,-1) rectangle (1.3,1);
%\clip(-1.5,-1.3) rectangle (1.5,1);
%\begin{axis} [axis lines=center]
\begin{scope}
\draw[scale=0.5,domain=-1.9:1.9,smooth,thick,variable=\x,color=mycolor1] plot ({\x},{0.75*\x^3-2*\x-1.});
%\plot [domain=-2:2, smooth, thick, color=blue] { x^3 - 2*x };
\end{scope}
%\end{axis}

\draw[-latex] (-1.5,-1.5) -- (1.8,-1.5) node[right] {\footnotesize{$x$}};
\draw[-latex] (-1.5,-1.5) -- (-1.5,0.8) node[left] {\footnotesize{$y=f(x)$}};

\draw[color=red] (-2.1,0.17) -- (1.3,0.17);
\draw[color=red] (-2.1,-1.15) -- (1.3,-1.15);

\draw[latex-latex, color=orange](-1.9,-1.15)--(-1.9,0.17) node[midway,left]{\footnotesize\textbf{{Wertebereich}}};

\draw[color=green] (-0.95,0.-1.9) -- (-0.95,-1.14);
\draw[color=green] (0.95,0.-1.9) -- (0.95,0.17);

\draw[latex-latex,color=green!50!black] (-0.95,-1.8) -- (0.95,-1.8) node[midway, below]{\footnotesize{Definitionsbereich}};
\end{tikzpicture}