Wie lässt sich der Graph einer Funktion in unterschiedliche Farben einteilen?

\documentclass[margin=2mm,tikz]{standalone}
\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{intersections}
\usepgfplotslibrary{fillbetween}

\begin{document}
\begin{tikzpicture}
  \begin{axis}[
    axis equal image,
    axis lines=middle,
    xmin=-2, xmax=15.5, % Axis limits
    ymin=-2, ymax=11.5,
    xtick={2,7,12},
    ytick=\empty,
  ]
  \addplot[no marks, smooth, samples=500,name path=f]
                    coordinates{(1,3) (2,3.5)(7,7)(8,1)(10,4.5)(11,3.5) (12,7.5) (13,8)};
    \draw[dashed, name path=i2](axis cs:2,0)--(axis cs:2,10);
    \draw[dashed, name path=i7](axis cs:7,0)--(axis cs:7,10);
    \draw[dashed, name path=i12](axis cs:12,0)--(axis cs:12,10);
      \path [
        name path=f2,
        intersection segments={
            of=i2 and f ,
            sequence={B1}
        }];
      \path [
      draw,blue,
        name path=2to7,
        intersection segments={
            of=f2 and i7 ,
            sequence={A0}
        }];
      \path [
        name path=f7,
        intersection segments={
            of=f2 and i7 ,
            sequence={A1}
        }];
      \path [
      draw,red,
        name path=7to12,
        intersection segments={
            of=f7 and i12 ,
            sequence={A0}
        }];
  \end{axis}
\end{tikzpicture}

\end{document}