The fun thing about working in the frequency domain is that the maths are really simple. For example, the effect of an equalizer is completely independent of the signal you're feeding it, it's just a simple multiplication of the signal (in frequency domain) with the equalizer frequency response.
What I'm getting at is that any visual equalizer already exactly shows what you want. So, if you have an equalizer that has settings for attenuating different frequencies (e.g., the one from windows media player), and you draw a nice smooth line through the settings, you already have the plot you want! Again, this is completely independent* of the signal you're feeding it.
Now what if you have an equalizer that has some vaguely named knobs like low, mid and high? Then you have a bit of a problem. Although it's possible to create the plot you want (divide the Fourier transform of the original and the equalized sound, and take the absolute value - i.e., what JCPedroza was getting at), chances are that it will be a very, very ugly plot. This is because, especially in music, many frequencies will not be present in the signal (if someone's singing an E, you won't have a lot of F in your signal), but above method will still try and get a frequency response at the frequency of a hypothetical F note. The result: a completely unreadable plot. The only 'easy' way to get a nice plot is to average a bunch of white noise fed through your equalizer.
*Completely independent in theory. In practice, there are always inaccuracies.