Question

which of the following are vertical asymptotes of the function: y=3cot(2 x)-4

Answer 1

x = 2pi
x= pi/3
x = pi/2
x = pi

Answer 2

where are the asymptotes for the cot graph?

Answer 3

where the zeros are?

Answer 4

no the asymptotes for the original cot graph

Answer 5

where the pis are

Answer 6

cot (2x) = cos(2x)/sin(2x)
V. Asympotes when sin(2x) = 0

The period of sin(2x) is pi, thus in the interval [0,pi] you have x = 0, pi/2 and pi being your vertical asympotes. i.e. every multiple of pi/2
Alternatively, cot(2x) simply is a horizontal compression of the cot(x) graph. So that the original cot is squeezed into of the normal period.
The period of tan (2x) and hence cot(2x) is pi/2, thus instead of the asymptotes occuring at 0, pi, 2pi, it will occur in half the interval, so 0, pi/2, pi etc,

Answer 7

A helpful note is that for y = Acot(Bx) + C, neither the A nor the C affect the position of the vertical asymptote as A is just a vertical dilation and C is a vertical translation. The B conveys a horizontal shift which will move the location of the vertical asymptote.