# Plotting these functions without encountering overflow errors

I want to plot the iterates of the function $f(x)=13xe^{-x}$ up to power $4$. So I am using the code Plot[{f[x], h[x], j[x], g[x], x}, {x, -0.3, 4}] where $f,h,j,g$ are the first, second, third, and fourth iterate of the function respectively. This sort of works, but overflow errors are thrown in my face: This is probably because the iterates get pretty complicated and probably give very large values. So, is there a better way to plot these functions?

• By iterates, do you mean h[x] == f[f[x]] etc.? What is the code you use to define f,h,j,g? – Marius Ladegård Meyer Mar 9 '16 at 7:47
• The trouble's coming from the left. Try Plot[Rest[NestList[13 # Exp[-#] &, x, 4]], {x, -0.03, 4}, Evaluated -> True] instead. – J. M.'s discontentment Mar 9 '16 at 7:48

As pointed out by J.M., the problem is with the negative x range. Particularly with your g[x]=f[f[f[f[x]]]], which evaluates to

28561 E^(-x - 13 E^-x x - 169 E^(-x - 13 E^-x x) x -
2197 E^(-x - 13 E^-x x - 169 E^(-x - 13 E^-x x) x) x) x


This very quickly approaches the $MaxNumber for negative values, $MaxNumber
f[f[f[f[-.06591]]]]
(* 1.605216761933662*10^1355718576299609 *)
(* -5.992559179678360*10^1344011404161905 *)


So you can either truncate the negative plotting range, or just use Quiet to suppress the error,

Plot[{f[x], f[f[x]], f[f[f[x]]], f[f[f[f[x]]]], x}, {x, -0.3, 4},
Evaluated -> True] // Quiet 