Question

Help?
Analyze the function f(x) = - 2 cot 3x. Include:
- Domain and range
- Period
- Two Vertical Asymptotes

Answer 1

@mathmale This one should be easy for you.. I got it wrong, though. :(

Answer 2

I left another comment for you at the end of our previous discussion. I'm not saying SSA will not work, but don't see the need to use it.

Answer 3

What part of the present problem has been difficult for you?

Answer 4

Analyze the function f(x) = - 2 cot 3x. Include:
- Domain and range
- Period
- Two Vertical Asymptotes
cos 3x
I see cot 3x and immediate change that to cot 3x =------------
sin 3x

and through having done so, see that we have vertical asy. whenever the denom. = 0.

Answer 5

How would you solve sin 3x = 0 for x? Remember that the period of a sine or cosine function y=a sin bx is 2Pi/b. In this example, b=3.

We calculate the period of a tangent or cotangent function differently:

The period of tan x is Pi/b (different from before); the period of tan bx is
pi/b. Does this help?

Answer 6

Sorry, I was AFK. I got the range, and period right, but I put:
Domain: AR#'s
Range: (-inf., inf)
Period: pi/3
VA: You have a VA everytime sin(x) is zero. So they are (pi, 0), (2pi, 0), (-pi, 0), (-2pi, 0).

And He said:
Ananda, You are correct for the Range and Period. Your vertical asymptotes should not be coordinates, and were affected by the Period change. The Domain is then restricted by the asymptotes. Mr. Harmon

Answer 7

cos 3x
I see cot 3x and immediate change that to cot 3x =------------
sin 3x

and through having done so, see that we have vertical asy. whenever the denom. = 0. In other words, to find the vertical asymptotes, let sin 3x = 0 and solve for x, for [0, pi/3). I know it's easier for me to say that than to do it.

You typed this: "VA: You have a VA every time sin(x) is zero. So they are (pi, 0), (2pi, 0), (-pi, 0), (-2pi, 0)." True, sin x = 0 for some of these five x values. BUT, in this problem, we're dealing with sin 3x, not with sin x. That's why Mr. Harman isn't accepting your answers for the vertical asymptotes.

You might want to graph sin 3x on the interval [0, pi/3. By doing so, you should be able to see quickly where sin 3x = 0. If you do this correctly, you'll find the x values at which sin 3x = 0 by inspection. I got x= {0, pi/6 and pi/3}. Important: please determine these values for yourself.

Answer 8

When I do it in my calculator, I get -2pi/3, -pi/3, 0, pi/3, and 2pi/3.

Answer 9

@mathmale

Answer 10

Hello!
One of the best things you could do would be to check your assumed answers by substituting them back into the original equation. In other words, determine whether y=-cot (3x) is UNDEFINED at those angles. If it is, then you've correctly identified where your graph has vertical asymptotes.

Answer 11

for example, if I take your solution -pi/3, and substitute it back into y=-cot (3x), I get y=-cot (-pi) = undefined, which seems to indicate that your solution is one of the places where the original function has a vertical asymptote.

It's important that you check each of the "answers" you've found, to ensure that y=-cot (3x) is actually undefined at each one, and that each one lies on the interval [0,pi/3]. (But you wouldn't be "wrong" if you chose "answers" that are outside of that interval.

Answer 12

If you like, try graphing y=cot x on the interval [0,2pi]. You'll see two full periods of this function on that interval. You'd have vertical asymptotes at x=0, x=pi, x=2pi.

How would the graph of y=cot (3x) be different?

First of all, the period would be shorter. The period would be pi/3, instead of pi.

You'd have vertical asymptotes that stem from x=0, x=pi and x=2pi:

the first one would be 0/3, or simply x=0.

The second would be x=pi/3.

The third wuold be x=2pi/3.

I strongly suggest that you actually graph y=cot (3x) on the interval [0,2pi] and see whether we have correctly predicted where the vert. intercepts will be.

Lastly, graph y=-cot (3x). this step is not really necessary, because this function will have exactly the same vertical asymptotes as does y=cot (3x).

Answer 13

I am absolutely lost.

Answer 14

Very sorry to hear that. At this point, I'd suggest y ou make an appointment to talk with your teacher face-to-face. If that's not possible, please try to formulate and share with me specific questions about the parts of this problem that have been most troublesome for you.