Question

Help would be appreciated!

Which of the following are vertical asymptotes of the function y=2ct(3x)+4? (Check all that apply)

A) x=0
B) x=2pi
C) x= +/- pi/2
D)x= pi/3

Answer 1

Is that \[\large y = 2cot(3x) + 4\]
?

Answer 2

Yes! @johnweldon1993

Answer 3

Hmm well since vertical asymptotes occur when the function approaches infinity, and that happens when a denominator = 0

We know that \(\large cot(3x) = \frac{1}{tan(3x)}\)

We ask ourselves when tan(3x) = 0?

Well to my knowledge, that only occurs at tan(0) so it looks like x = 0 is your vertical asymptote here

Answer 4

Thank you! Would that be the only one or is there another possibility? @johnweldon1993

Answer 5

Well from what the graph looks like, it looks as if there is a repeating vertical asymptote every \(\large \frac{\pi}{3}\)

But lets check that

Answer 6

\[\large y = \frac{2}{tan(3x)} + 4\]
\[\large y = \frac{2cos(3x)}{sin(3x)} + 4\]

So that is where we see that at x = 0 we approach infinity...but now lets check \(\large \frac{\pi}{3}\)

\[\large y = \frac{2cos(\frac{3\pi}{3})}{(sin\frac{3\pi}{3})} + 4\]
\[\large y = \frac{2cos(\pi)}{sin(\pi)} + 4\]

Ahh and also \(\large sin(\pi) = 0\) so yes also one every \(\large \frac{\pi}{3}\)

Answer 7

haha now that I look, another one of your answers is correct!

Answer 8

So as you can see...the main thing I look for is when the denominator = 0

The denominator here is \(\large sin(3x)\)

So whenever that = 0 we have a vertical asymptote

Answer 9

We know \(\large sin(0) = 0\)
\[\large sin(\pi) = 0\]
\[\large sin(2\pi) = 0\] and also any multiple of \(\large \pi\) = 0 when it comes to sin...so It looks like A, B, and D are ALL correct here

Answer 10

Thank you so much!!!

Answer 11

No problem!