Hi,

there are several "issues" here. First of all

(x - 50000)^4.51846

is complex for x<50000, e.g.

(x - 50000)^4.51846 /. x -> 2
is -9.88935*10^19 + 1.70333*10^21 I.

Plot does not plot complex numbers.The "interesting part of your graph is for x>50000.

Also, you should plot f[x] instead of "f".

f[x_] := ((x - 50000)^4.51846) (E^(50000 - x)) (4.6924^-7)
Plot[f[x], {x, 50000, 50050}, PlotRange -> All]

does work and gives a reasonable output:

So, if you plot it for x< 50000 it will not produce a useful output, because the Plot function is not made to plot complex functions.

Furthermore, the values that you want to plot are insanely large. Look at this:

Table[Evaluate[f[x]], {x, 0, 5}]

{-1.046106944790515*10^21730 + 
  1.801802763355185*10^21731 I, -3.848064616838928*10^21729 + 
  6.627862949115713*10^21730 I, -1.415495933981097*10^21729 + 
  2.438034178117325*10^21730 I, -5.206847948258534*10^21728 + 
  8.968215982373779*10^21729 I, -1.915319207666480*10^21728 + 
  3.298924128423410*10^21729 I, -7.045428821964528*10^21727 + 
  1.213496687279907*10^21729 I}

In the interesting regime 50000<x<50050 the values are very small. It will be difficult to have a reasonable representation over the entire domain.

Cheers, Marco