Question

Graph the function.

Answer 1

well, first of all, it's an absolute value so you know that y is always non-negative. That quickly eliminates 2 of the choices.

After that - consider what happens around x=0. If x=0 then you have |cot(0)|. Since cotx = 1/tanx, think about what that means when x=0.

Does that help?

Answer 2

So I can eliminate B and C?

Answer 3

And I think I would choose D.

Answer 4

Well, cotangent is the same as cosine/sine. The main difference between your two positive graphs is one is defined at 0 and one is undefined at 0. So the way to know which one is to look at the denominator of cotangent, which is sine. At x = 0, what is sine?

Answer 5

I'm lost

Answer 6

What is cotangent?

Answer 7

cot is cotangent

Answer 8

Oh

Answer 9

You were on the right track - eliminate B and C because they include negative values for y. Like @Psymon said, think about what happens to cotx at x=0.

Answer 10

The key to this problem is knowing what sin(0) =

Answer 11

@ExplainItLikeImFive what class is this for? Seems like a pretty advanced problem if you aren't familiar with the trig functions...?

Answer 12

This is Pre-Calc

Answer 13

I think at this point I would choose A.

Answer 14

Correct. The reason is that sin(0) is 0. And since the cot function is the same as cos/sin, x = 0 would give us a 0 in the denominator! we can't have that, so that means your function is undefined at 0 :P

Answer 15

Is it expected that you've already had some trig? And have you?

Yes, A, because sin(0)=0, so cot(0) is undefined and therefore has a vertical asymptote at x=0. Also, the period of y=cot(x) is pi, so for y=cot(x/4), you would have a period of 4pi, which is what appears in the graph for A.

Answer 16

Yeah I have taken some trig, but as you can tell I did't retain much.

Answer 17

Thanks to you both.

Answer 18

Mhm :3