Plotting arrows at the edges of a curve

Question

Inspired by this question at ask.sagemath, what is the best way of adding arrows to the end of curves produced by Plot, ContourPlot

Answer 1

The following construct has the advantage of not messing with the internal structure of the Graphics structure, and is more general than the one suggested in ask.sagemath, as it manage PlotRange and infinities better.

f[x_] = Gamma[x]

{plot, evals} = 
  Reap[Plot[f[x], {x, -2, 2}, Axes -> False, Frame -> True, 
    PlotRangePadding -> .2, EvaluationMonitor :> Sow[{x, f[x]}]]];

{{minX, maxX}, {minY, maxY}} = Options[plot, PlotRange] /. {_ -> y_} -> y; 
ev = Select[evals[[1]], minX <= #[[1]] <= maxX && minY <= #[[2]] <= maxY &];
seq = SortBy[ev, #[[1]] &];
arr = {Arrow[{seq[[2]], seq[[1]]}], Arrow[{seq[[-2]], seq[[-1]]}]};

Show[plot, Graphics[{Red, arr}]]

Edit

As a function:

arrowPlot[f_, interval_] := Module[{plot, evals, within, seq, arr},
   within[p_, r_] :=
    r[[1, 1]] <= p[[1]] <= r[[1, 2]] &&
     r[[2, 1]] <= p[[2]] <= r[[2, 2]];

   {plot, evals} = Reap[
     Plot[f[x], Evaluate@{x, interval /. List -> Sequence},
      Axes -> False,
      Frame -> True,
      PlotRangePadding -> .2,
      EvaluationMonitor :> Sow[{x, f[x]}]]];

   seq = SortBy[Select[evals[[1]],
      within[#, 
        Options[plot, PlotRange] /. {_ -> y_} -> y] &], #[[1]] &];

   arr = {Arrow[{seq[[2]], seq[[1]]}], Arrow[{seq[[-2]], seq[[-1]]}]};
   Show[plot, Graphics[{Red, arr}]]
   ];

arrowPlot[Gamma, {-3, 4}]  

Still thinking what is better for ListPlot & al.