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Y=4cot(3x−3π/4)−1 whats is vertical asymptotes

User Taukheer
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1 Answer

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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.

User Maess
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