Which of the following are vertical asymptotes of the function y = 3cot(1/2x) - 4?

x=0 or ±2 nπ where n belongs to natural numbers.

Step-by-step explanation:

The " vertical asymptote " is a vertical line that the graph of a function approaches but never touches. To find the vertical asymptotes of a rational function we set denominator=0.

We are given function y=3 cot((1/2)x)-4

which could also be written as

for denominator to be equal to 0 we must have sin((1/2)x)=0

⇒ (1/2)x=0

⇒   x=0 or ±2 nπ where n belongs to natural numbers.

Hence, the vertical asymptotes of the given function is  x=0 or ±2 nπ where n belongs to natural numbers.

Equation of the line: y=2

Step-by-step explanation:

So, the horizontal line will have the equation y=2 because the y-coordinate of the point is 2.