Question

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

Answer 1

http://www.wolframalpha.com/input/?i=range+and+domain++f%28x%29+%3D+-+2+cot+3x

Answer 2

@integralsabiti how would you read that can you help me read how you would saw what the domain and range and other things are

Answer 3

I know the range is all real

Answer 4

and I dont know what the vertical asymtote is either the two vertical asymptotes

Answer 5

@amistre64 help pls :)

Answer 6

since cotangent is a ratio of cos to sin; the verts are defined when sin is zero

Answer 7

sin is zero at 0 and 180 degrees; so when is 3x = 0 or 180 degrees?

Answer 8

the vertical asymptotes are the open circles on the number line of the link that integral provided

Answer 9

im confused which one are we doing first the domain ?

Answer 10

For the options @amistre64 I know the period is "pi/3" and I know The range is all real numbers I am having a hard time finding the two V.A. and the domain

Answer 11

there are an infinite number of VAs, they only want you to provide 2 of them

Answer 12

whenever 3x = 0 or pi, this thing becomes undefined and pops out a VA

Answer 13

so what two should I say ?

Answer 14

when does 3x=0? use that x value for a VA

when does 3x=pi? use that x value for a VA

Answer 15

can i say one is 0 and another can be 2pi n/3?? does that work?

Answer 16

0 is good

the "n" doesnt make it specific; 2pi/3 is fine tho

Answer 17

the domain excludes all the VAs, so that would need to be generalized as: n pi/3

Answer 18

The range of this equation is all real numbers and the domain is n pi/3
The Period is pi/3
and lastly the two vertical asymptotes are 0 and 2pi/3
Is this a good answer?

Answer 19

domain needs some attention

the way you have stated it; it says that the usable values of x that we can use are only integer values of n pi/3; when these values are actually the ones we need to avoid

Answer 20

The domain is all Real values such that for any integer "n", x DOES NOT equal: n pi/3

Answer 21

sorry Im confused again so I should say its all real values as well as the range or ?

Answer 22

Does "domain" define all the values that we can use?

Answer 23

the domain is all real numbers except vertical asymptotes (sorry for interrupting :)

Answer 24

\[cot(x)=\frac{cos(3x)}{sin(3x)}~:~such~that~x\ne\frac{\pi}{3}n~for~any~integer~"n"\]why? becasue:

sin(3n pi/3) = sin(n pi) = 0

Answer 25

so like integersabiti said It would be all real numbers except for the VA's right @amistre64

Answer 26

correct.

Answer 27

except for ALL the VAs, not just the 2 that you defined

Answer 28

integralsabiti means 'intagral constant ' .What you said is (integersabiti) much more interesting :D 'integer constant '

Answer 29

THANK YOU SO MUCH !