Find the Asymptotes y=-3tan(1/2x)

Problem

y=−3*tan(1/2*x)

Solution

1. Identify the standard form of the tangent function y=A*tan(B*x) where B=1/2

2. Recall that the vertical asymptotes for the parent function y=tan(θ) occur where the argument θ is an odd multiple of π/2

3. Set up the equation for the asymptotes by setting the argument of the tangent function equal to the general expression for vertical asymptotes.

1/2*x=π/2+n*π

4. Solve for x by multiplying both sides of the equation by 2

x=2*(π/2+n*π)

5. Simplify the expression to find the general formula for the vertical asymptotes, where n is any integer.

x=π+2*n*π

Final Answer

x=π+2*n*π,where *n∈ℤ

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