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Example Question #1 : Find The Equations Of Vertical Asymptotes Of Tangent, Cosecant, Secant, And Cotangent Functions
Given the function , determine the equation of all the vertical asymptotes across the domain. Let be an integer.
For the function , it is not necessary to graph the function. The y-intercept does not affect the location of the asymptotes.
Recall that the parent function has an asymptote at for every period.
Set the inner quantity of equal to zero to determine the shift of the asymptote.
This indicates that there is a zero at , and the tangent graph has shifted units to the right. As a result, the asymptotes must all shift units to the right as well. The period of the tangent graph is .