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How do you "find the range of a function for a given domain ?

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The domain of a function is the numbers on the x coordinate that the function can be. The range is the same, but for the y axis.
So for the function you gave, if the domain is all numbers between -1 and 3, you plug in those numbers
ƒ(-1) = 3x + 2 → 3(-1) + 2 = -5
ƒ(3) = 3x + 2 → 3(3) + 2 = 11
and the output is the range.
In this case, the domain would be all numbers between -1 and 3, and the range would be all numbers between -5 and 11


I think you can have the domain as y if y is the independant variable although x is almost always the independant variable. Right? :P
Yes. The domain is the independent variable, whether you call it x, y, or Q.