Question

Which is an asymptote of the graph of the function y = cot ( x - 2pi / 3 )

A) x = - 2 pi / 3

B) x = - pi / 3

C) x = - 4 pi / 3

C) x = 7 pi / 3

Answer 1

The answer to the equation is b

Answer 2

Answer with explanation:

we have to find the Asymptote of the function:

`y=\cot(x-(2\pi)/(3))`

As period of cot x is equal to [-π, π].

`x-(2\pi)/(3)=0\\\\x=(2\pi)/(3)\\\\ x-(2\pi)/(3)=\pi\\\\x=(2\pi)/(3)+\pi \\\\x=(5\pi)/(3) \\\\x=\cot(2\pi -(\pi)/(3))\\\\x=(-\pi)/(3)`

You can find asymptote by drawing the graph of

`y=\cot(x-(2\pi)/(3))`

There are two Asymptotes

`1.\rightarrow x= (-\pi)/(3)\\\\2..\rightarrow x= (2\pi)/(3)`

Out of the four option

⇒Option B

`x=(-\pi)/(3)` is one asymptote of the graph.