\documentclass{standalone}

\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}