\documentclass{standalone}
\usepackage{luamplib}
\begin{document}
\mplibtextextlabel{enable}
\begin{mplibcode}
input colorbrewer-rgb
ahangle := 30;
beginfig(1);
  numeric u;
  u = 42;
  path xx, yy, f;
  xx = (1/4 left -- 17/4 right) scaled u;
  yy = (1/4 down -- 9/4 up) scaled u;

  f = ((15/32,32/15) for x = 1/2 step 1/8 until 33/8: .. (x,1/x) endfor) scaled u;

  path A; A = % keep next on it's own line....
  buildcycle(yy shifted (u,0), f, yy shifted (2.71828u,0), xx)
  ;
  fill A withcolor Blues 8 2;

  drawoptions(withcolor 3/4);
  for x=1 upto 4: 
    draw yy shifted (x*u,0) cutafter (xx shifted (0, ypart point 0 of f)); 
  endfor
  for y=1 upto 2: 
    draw xx shifted (0,y*u) cutafter (yy shifted (xpart point infinity of f,0)); 
  endfor

  drawoptions();
  draw f withcolor Reds 8 7;
  drawarrow xx;
  drawarrow yy;

endfig;
\end{mplibcode}
\end{document}