I have tried increasing Samples to 700, and it helped a little. I saw that my green f(x) is closer to the asymptote x=-1,x=1. However, it is not close enough. Is there any way to make the green f(x) approaches x=+-1 until ymax and ymin?

Also, I am looking for the way to automatically label axis all digit numbers -7,-6,...,7 without specifying like this.

 \begin{axis}[axis lines=middle,xlabel=$ x $,ylabel=$ y 
 ytick={-0.9,0.9},scale=2, restrict y to domain=-7:7,
 \addplot[domain=-7:0,draw=green,width=2pt] {x+ln((x-1)/(x+1))};
\addplot[domain=0:7,draw=green,width=2pt] {x+ln((x-1)/(x+1))};
\addplot[only marks] coordinates {(-2,-0.9)(2,0.9)};
\addplot[smooth,no marks,draw=blue] coordinates {(-1,-7)(-1,7)[x=-1]};
\addplot[smooth,no marks,draw=blue,width=2pt] coordinates {(1,-7)(1,7) 
 \draw[green](3,4) node{$ f(x) $};

enter image description here

  • 2
    It seems no matter how far does the green curve go it IS covered by the blue line. Isn't that exactly what you want? – Symbol 1 Apr 8 '18 at 3:21
  • @Symbol1 the green line doesnt go as up, and down, as it should go. – Panha Apr 8 '18 at 4:47
  • Was my answer helpful to solve your question? If so, please consider upvoting (by clicking on the arrows next to the score) and/or marking it as the accepted answer (by clicking on the checkmark ✓). If not, please let us know what still is unclear. – Stefan Pinnow Apr 10 '18 at 20:36

The trick is to use the starred version of restrict y to domain and to use proper domains to get the desired result.

For details please have a look at the comments in the code.

% used PGFPlots v1.16
        axis lines=middle,
        xtick distance=2,
        % use the stared version of the command, which uses the given limit
        % value if the real value exceeds the given range instead of
        % not showing it at all
        restrict y to domain*=-7:7,
        % (no need to use that much samples)

        % changed the domain limits to something a little bit "larger" than
        % the undefined points at x=-1 and x=1
        \addplot [ultra thick,green,domain=-7:-1.0001] {x+ln((x-1)/(x+1))};
        \addplot [ultra thick,green,domain=1.0001:7] {x+ln((x-1)/(x+1))};

        \draw [green](3,4) node{$ f(x) $};

        \addplot [only marks] coordinates {(-2,-0.9)(2,0.9)};

        \addplot [blue] coordinates {(-1,-7)(-1,7)};
        \addplot [blue] coordinates {(1,-7)(1,7)};

image showing the result of above code

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