Question

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

A) x = - 2 pi / 3

B) x = - pi / 3

C) x = - 4 pi / 3

C) x = 7 pi / 3

Answer 1

The asymptote of the graph of the function y = cot(x - 2π/3) is x = -2π/3.

Step-by-step explanation:

The function y = cot(x - 2π/3) has vertical asymptotes whenever the value inside the cotangent function is equal to an odd multiple of π. In this case, x - 2π/3 = nπ, where n is an odd integer. Let's solve for x to find the asymptotes:

1. x = nπ + 2π/3
2. Since we're given options in terms of fractions of π, we need to simplify this answer:
   x = nπ + 2π/3 = (3n + 2)π/3

Therefore, the option that represents an asymptote of the graph of the function is x = -2π/3.

Answer 2

B

Step-by-step explanation:

x= -pi/3