#title: function that
#author: jj, irene,...

#let:

 x[2]  = [-4,-3,-2,1,2,3,4];
 lll   = [0,1];
 lll2  = {#x[#lll]};
 v     = [-3 , -2 , -3 ,1,2,3,4];
 x0    = [ -0 -1 , 0 , 1, 2 ];

    f2 ={{1/(x-#x[0]) + 1/(x-#x[1]) + #v}} ;
    f0 = maxima{1/(x-#x[#lll]) + 1/(x-#x[0]) + 1/(x-#x[1]) + #v} ;
    f1 = maxima{ratsimp(#f0)} ;
f ftex = #f1;


#jjj

f   f2 = {{ratsimp(1/(x-#x[0]) + 1/(x-#x[1]) + #v)}} ;
  fstr = # f2;

#usepackage
\usepackage{pgfplots}
\usepackage{tikz}

#question

lll = #lll #lll2 #x[]

 $#f2 = #f0 = #f1 = #ftex$

Consider a function $f$ (== $#ftex$) whose graphic is

  \begin{tikzpicture}
     \begin{axis}[
       restrict y to domain=-7:7,
       grid,
       samples=1000,
       minor tick num=1,
       xmin = -7, xmax = 7,
       ymin = -6, ymax = 6,
       unbounded coords=jump,
       axis x line=middle,
       axis y line=middle]
      \addplot[color=red,mark=none,domain=-7:7] {#f1};
    \end{axis}
  \end{tikzpicture}

The asymptotes are integer numbers.

\begin{enumerate}
\item Write the equation of the asymptotes.
\item Write a function ??? with identical assimptotical behaviour.
\end{enumerate}

#result

  for example: $f(x) = #f0 = #ftex$

  %% for example: $f(x) = # fstr # f2$