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

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

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

Answer

Answer:

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

Explanation:

Step1: Recall cotangent asymptote formula

The cotangent function $y = \cot(u)$ has asymptotes at $u = n\pi$, where $n\in\mathbb{Z}$. For the function $y=\cot(x - \frac{2\pi}{3})$, set $x-\frac{2\pi}{3}=n\pi$.

Step2: Solve for $x$

$x=n\pi+\frac{2\pi}{3}$.

Step3: Find the correct option

When $n = - 1$, $x=-\pi+\frac{2\pi}{3}=-\frac{\pi}{3}$.