which is an asymptote of the graph of the function $y = cot(x-\frac{2pi}{3})$?\n$x =-\frac{2pi}{3}$\n$x…

which is an asymptote of the graph of the function $y = cot(x-\frac{2pi}{3})$?\n$x =-\frac{2pi}{3}$\n$x =-\frac{pi}{3}$\n$x =\frac{4pi}{3}$\n$x =\frac{7pi}{3}$

which is an asymptote of the graph of the function $y = cot(x-\frac{2pi}{3})$?\n$x =-\frac{2pi}{3}$\n$x =-\frac{pi}{3}$\n$x =\frac{4pi}{3}$\n$x =\frac{7pi}{3}$

Answer

Explanation:

Step1: Recall cotangent asymptote formula

The cotangent function $y = \cot(u)$ has asymptotes when $u = n\pi$, where $n$ is an integer. For the function $y=\cot\left(x - \frac{2\pi}{3}\right)$, we set $x-\frac{2\pi}{3}=n\pi$.

Step2: Solve for x

Add $\frac{2\pi}{3}$ to both sides of the equation $x-\frac{2\pi}{3}=n\pi$. We get $x=n\pi+\frac{2\pi}{3}$. When $n = 1$, $x=\pi+\frac{2\pi}{3}=\frac{3\pi + 2\pi}{3}=\frac{5\pi}{3}$. When $n=- 1$, $x=-\pi+\frac{2\pi}{3}=\frac{-3\pi + 2\pi}{3}=-\frac{\pi}{3}$.

Answer:

$x =-\frac{\pi}{3}$