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f(x) = - 2 cot 3x please someone help me find the domain and range of this functions

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Do you know the domain and rain for cot?
that its undefined because its domain in standard form is all real #s except pi? I am not sure, I am guessing
Right, the domain of cot(x) is all reals except for integer multiples of pi. So not at 0, pi, 2pi, ...

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So if this is cot(3x), then 3x cannot equal n*pi. Now solve for x
do I solve for x by setting 3x = 0?
No. What @Tonks means is "solve of x in terms of n and pi", I believe. He's stating an easy statement in a very formal manner.
No, I mean in a statement like 3x = n*pi, isolate x on one side and everything else on the other by dividing by 3...
Yep. Exactly what I said. ;)
Ok, but how do I get the domain or range from that?
Take the domain of the basic function and think of it geometrically.
|dw:1350961916817:dw| Here is -cotx
Now if you are familiar with transformations, then you know a multiple of x compresses the graph along the x-axis
That compression will move the asymptotes, like an accordion, toward the origin.

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