Question

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

Answer 1

The answer to the equation is b

Answer 2

Answer with explanation:

we have to find the Asymptote of the function:

  $y=\cot(x-\frac{2\pi}{3})$

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

 $x-\frac{2\pi}{3}=0\\\\x=\frac{2\pi}{3}\\\\ x-\frac{2\pi}{3}=\pi\\\\x=\frac{2\pi}{3}+\pi \\\\x=\frac{5\pi}{3} \\\\x=\cot(2\pi -\frac{\pi}{3})\\\\x=\frac{-\pi}{3}$

You can find asymptote by drawing the graph of

     $y=\cot(x-\frac{2\pi}{3})$

There are two Asymptotes

$1.\rightarrow x= \frac{-\pi}{3}\\\\2..\rightarrow x= \frac{2\pi}{3}$

Out of the four option

⇒Option B

          $x=\frac{-\pi}{3}$ is one asymptote of the graph.