Find the Asymptotes y=tan(3/4x)

Math
Combine and .
For any , vertical asymptotes occur at , where is an integer. Use the basic period for , , to find the vertical asymptotes for . Set the inside of the tangent function, , for equal to to find where the vertical asymptote occurs for .
Solve for .
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Multiply both sides of the equation by .
Simplify both sides of the equation.
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Simplify the left side.
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Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Simplify .
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Cancel the common factor of .
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Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine and .
Set the inside of the tangent function equal to .
Solve for .
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Multiply both sides of the equation by .
Simplify both sides of the equation.
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Simplify the left side.
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Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Simplify .
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Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine and .
The basic period for will occur at , where and are vertical asymptotes.
Find the period to find where the vertical asymptotes exist.
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is approximately which is positive so remove the absolute value
Multiply the numerator by the reciprocal of the denominator.
Combine and .
Move to the left of .
The vertical asymptotes for occur at , , and every , where is an integer.
Tangent only has vertical asymptotes.
No Horizontal Asymptotes
No Oblique Asymptotes
Vertical Asymptotes: where is an integer
Find the Asymptotes y=tan(3/4x)

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