plotting - Can you plot pure function without specifying variable?

Given a pure function, e.g. f=Sin[#]&, it is possible to plot it with introducing an arbitrary local variable, e.g.,

Plot[f[x],{x,0,1}]

However, the introduction of a variable x seems unnecessary. Is it possible to plot this without specifying a name for the variable? If not, is there a good reason why this functionality doesn't exist?

Answer

Yes, you can plot it, but not using Plot. For example, you could map the function over a range of values and then use ListLinePlot:

With[{xmin = 0, xmax = 4π},
 ListLinePlot[f/@Subdivide[##,100],DataRange->{##}]&[xmin,xmax]
]

This uses the new function Subdivide with 100 plot points.

The reason why Plot requires you to specify a dummy variable is that it takes expressions and not functions as its argument. Therefore, the plot variable is not identifiable by a slot, and you need to specify it by naming the plot variable.