Final answer:
Vertical asymptotes of the function y=4cot(3x-3π/4)-1 occur at x = π(n + 1/4)/3, where n is any integer since these are the values where the cotangent function is undefined.
Step-by-step explanation:
The question is asking to find the vertical asymptotes of the function y=4cot(3x−3π/4)−1.
To find the vertical asymptotes of a cotangent function, you need to determine where the cotangent function is undefined, which occurs where the tangent function has a value of zero.
The general form of a cotangent function is cot(θ) = θ + (n π), where n is an integer, and θ is the angle where the tangent is zero.
For the function 4cot(3x−3π/4), we set the inside of the cotangent function to be n π, where n is an integer.
Therefore, 3x - 3π/4 = nπ.
Solving for x gives us vertical asymptotes at x = π(n + 1/4)/3, where n is an integer.
Remember that the function will have an infinite number of vertical asymptotes where this condition is met, as n can be any integer.