A question about Manipulate command in Mathematica

[kindlychung]

This works:

Manipulate[Plot[E^(n*x), {x, -10, 10}], {n, 1, 10}]

This doesn't:

f[x_] := E^(n*x);
Manipulate[Plot[f[x], {x, 1, 10}], {n, 1, 10}]

Why?
(I used Mathematica 7.0)

 

[CompuChip]

Then again, this does:

Subscript[f, n_][x_] := E^(n*x);
Manipulate[Plot[Subscript[f, n][x], {x, 1, 10}], {n, 1, 10}]

Apparently the n in the definition of f[x] is not the same n as that in Manipulate. When you execute

Subscript[f, n_][x_] := E^(n*x);
Manipulate[Plot[Subscript[f, n][x], {x, 1, 10}] // Hold, {n, 1, 10}]

you will see that the running n is a temporary variable (FE`n$$27, or something like that) different from the Global`n that f[x] uses. When you pass n to f[x] as well, by defining f_n[x] or f[n, x], it works.