Find the Asymptotes y=2cot(3x)+4

Problem

y=2*cot(3*x)+4

Solution

1. Identify the parent function and its properties. The function is a transformation of y=cot(u) which has vertical asymptotes where the input u is an integer multiple of π

2. Set up the equation for the vertical asymptotes by setting the argument of the cotangent function, 3*x equal to n*π where n is any integer.

3*x=n*π

3. Solve for x by dividing both sides of the equation by 3

x=(n*π)/3

4. Determine if there are any horizontal asymptotes. Since the range of the cotangent function is (−∞,∞) the vertical stretch and shift do not create horizontal boundaries.

No horizontal asymptotes

Final Answer

x=(n*π)/3

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