## marasofia1616 2 years ago f(x) = - 2 cot 3x please someone help me find the domain and range of this functions

1. Ahaanomegas

Do you know the domain and rain for cot?

2. marasofia1616

that its undefined because its domain in standard form is all real #s except pi? I am not sure, I am guessing

3. Tonks

Right, the domain of cot(x) is all reals except for integer multiples of pi. So not at 0, pi, 2pi, ...

4. Tonks

So if this is cot(3x), then 3x cannot equal n*pi. Now solve for x

5. marasofia1616

do I solve for x by setting 3x = 0?

6. Ahaanomegas

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.

7. Tonks

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...

8. Ahaanomegas

Yep. Exactly what I said. ;)

9. marasofia1616

Ok, but how do I get the domain or range from that?

10. Ahaanomegas

Take the domain of the basic function and think of it geometrically.

11. Tonks

|dw:1350961916817:dw| Here is -cotx

12. Tonks

|dw:1350962021979:dw|

13. Tonks

Now if you are familiar with transformations, then you know a multiple of x compresses the graph along the x-axis

14. Tonks

That compression will move the asymptotes, like an accordion, toward the origin.