# Why doesn't this plot work?

I'm trying to plot the output of an integral, but the plot does not show. The axes show, but not the plot itself. I have tried what I felt was a reasonable range of axes values, but the result is the same. The following is what I'm working with:

function = Exp[I k x] C Exp[-a x^2];

Integrate[function, {x, -\[Infinity], \[Infinity]}]

ConditionalExpression[(C E^(-(k^2/(4 a))) Sqrt[\[Pi]])/Sqrt[a],
Re[a] > 0]

output = %;

Plot[output, {k, -10, 10}]


What is wrong here? Anyone have some suggestions on how to obtain the plot? I'm compelled to think there is some kind of 'automatic' range parameters that can be used with general plots, but I have not found anything in the Documentation center of Mathematica, nor have I found any FAQs here that I've found helpful either.

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I'm almost sure I've seen several questions like these, but can't find them at the moment. – Sjoerd C. de Vries Sep 27 '12 at 19:11

It is because C and a are undefined; if they are set to something, a plot is obtained, e.g.
function = Exp[I k x] C Exp[-a x^2];