Question

HELP
What is the domain of -2 cot 3x?

Answer 1

@mathstudent55 @whpalmer4

Answer 2

@mathmale

Answer 3

http://www.wolframalpha.com/input/?i=What+is+the+domain+of+-2+cot+3x

Answer 4

What is the domain of -2 cot 3x?
"Domain" in this context refers to "acceptable or permitted input values to the function in question." BG: Have you successfully found domains before?

Answer 5

While this paper is a bit too technical for our purposes, it just might help you figure out the domain of cot x:

http://faculty.atu.edu/mfinan/1203/Lecture15.pdf

The domain of cot 3x is different.

\[\cot 3x = \frac{ \cos 3x }{ \sin 3x }\]
which is not defined at any x value at which sin 3x = 0.

If you can find those x values, then the DOMAIN of cot 3x would be "all real numbers EXCEPT for the ones you've just identified."

Try to link up with me tomorrow if you need further help with this.

Answer 6

I put all real numbers as long as 3x > pi times n. That's what it said on that wolf website.. It made sense when my boyfriend showed me an example. Is that technically right?

Answer 7

I started with cot x as an example; the period of cot x is simply pi. As I believe you'v e seen on wolframalpha,com, the function cot x goes to +infinity as x nears 0 and to -infinity as x nears pi. Thus, the x-values at which cot x is undefined are 0 plus or minus an integer multiple of pi, and pi plus or minus an integer multiple of pi. This must sound pretty abstract. I'd suggest you ask questions if any of my statements don't make sense to you.

Answer 8

I think I'm at least halfway caught up.

Answer 9

Now for y=cot 3x. Same function, but different argument. That multiplier, 3, in 3x, will shorten the period of the cot function to 1/3 what it was before (pi). So now the period of y=cot x is pi/3.

Applying what I wrote earlier:

Thus, the x-values at which cot x is undefined are 0 plus or minus an integer multiple of pi/3, and
pi/3 plus or minus an integer multiple of pi/3.

You could graph cot 3x on wolframalpha and obtain the x-values at which cot 3x is undefined directly from that graph.

By all means let me know if you need and want further clarification.

Answer 10

So what does the -2 do to it? Is what I put wrong?

Answer 11

@mathmale

Answer 12

That coefficient, -2, does affect the shape of the graph, but does NOT affect where the function cot 3x is undefined. You can safely ignore the -2 in this particular problem.

Answer 13

Okay. So what I put should be considered right?

Answer 14

What is the domain of -2 cot 3x?
As before, you can safely ignore the -2.
Reviewing what we've discussed, please write below what YOU think is the correct response to "What is the domain of -2 cot 3x?"

Answer 15

I put all real numbers as long as 3x > pi times n...

Answer 16

Thanks for trying. There's no need for an inequality sign (>) here.

What would probably help most would be for us to identify some of the FORBIDDEN values of x for the function y=cot 3x: The first few are {0, pi/9, 2pi/9, 3pi/9}.

I know I didn't mention this earlier. Again, I'd suggest that you graph cot 3x on wolframalpha.com, and compare the locations of the vertical asymptotes of that graph to the ones I've just identified, above.

Answer 17

I did.. And that's what it gave me for the domain for my problem.

Answer 18

So, please type out what you believe is the answer to your question about the domain of y=-2 cot 3x. I'll give you feedback on that.

Answer 19

What I put. That's exactly what I typed as my answer. Me and him looked up how to find domain restrictions on my calculator. "I put all real numbers as long as 3x > pi times n... "

Answer 20

What is the domain of -2 cot 3x?

There are several ways in which you could write your answer:

You could either write the domain restrictions (which you seem to be doing), or
write the INTERVALS on which -2 cot 3x is defined.

If you prefer to write out domain restrictions, then the following would be correct:

\[x \neq 0 \pm n*(\pi/9).for.n:\pm 0, 1, 2, 3, ...\]

Answer 21

On the other hand, if you prefer to write out the intervals on which cot 3x is defined, you might do this:

\[(0,\pi/9) U (\pi/9,2\pi/9) U (2\pi/9,\pi/3) \]and so on.

Answer 22

Your choice.

Answer 23

Oh, Lord. Domain and range are two things I could never understand..