\begin{tikzpicture} [
  % declare function={
  %   func(\x)= (\x >= -3) * (\x^2)   +
  %    and(\x < -3) * (-\x);
  % }
]
  \begin{axis}[
    xlabel = $x$, ylabel = $y$,
    width = 10cm, height=10cm,
    axis lines = middle,
    grid,
    xmin=-9, xmax=5,
    ymin=-7, ymax=7,
    legend pos=outer north east,
    legend style={cells={align=left}}
  ]

    \addplot [
      blue,
      no marks,
      domain= -3:100
    ]{2*x};
    \addplot [
      blue,
      no marks,
      domain= -100:-3
    ]{-x};
    
    \addplot+[blue,mark=*,mark options={fill=white}] (-3,3);
    \addplot+[blue,mark=*] (-3,-6);

    \addlegendentry{$g(x) = \begin{cases}
      2x\text{, hvis } x \geq -3 \\
      -x \text{, hvis } x < -3
    \end{cases}$ \\}
    
  \end{axis}
\end{tikzpicture}