Question

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

Answer 1

Answer:

B. x = -pi/3

Step-by-step explanation:

this is the correct answer on ed-genuity, hope this helps you! :)

Answer 2

$\bf y=cot\left(x-\frac{2\pi }{3} \right)\implies y=\cfrac{cos\left(x-\frac{2\pi }{3} \right)}{sin\left(x-\frac{2\pi }{3} \right)}$

now, if the denominator turns to 0, the fraction becomes undefined, and you get a "vertical asymptote" when that happens, so let's check when is that

$\bf sin\left(x-\frac{2\pi }{3} \right)=0\implies sin^{-1}\left[ sin\left(x-\frac{2\pi }{3} \right) \right]=sin^{-1}(0) \\\\\\ x-\frac{2\pi }{3}= \begin{cases} 0\\ \pi \end{cases}\implies \measuredangle x= \begin{cases} \frac{2\pi }{3}\\ \frac{5\pi }{3} \end{cases}$

now, at those angles, the function is asymptotic, check the picture below