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 $n\in\mathbb{Z}$. For the function $y=\cot\left(x - \frac{2\pi}{3}\right)$, 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 $x=n\pi+\frac{2\pi}{3}$.

Step3: Find a specific asymptote

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

Answer:

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