For what values of x, if any, does #f(x) = tan((3pi)/4-9x) # have vertical asymptotes?

1 Answer
Oct 11, 2017

Answer:

# x=-pi/36# and #x=-pi/18# for #0<=theta<=(2pi)#

Explanation:

Vertical asymptotes occur at values for which the function is undefined. Using this, we know that:

#0<=theta<=(2pi)#

as #theta-> pi, tan(theta)-> oo#

also as #theta-> (3pi)/2, tan(theta)-> -oo#

This means that if:

#((3pi)/4-9x)= pi or (3pi)/2#

The function will be undefined, and vertical asymptotes will occur.

So:

#(3pi)/4-9x= pi=> x=-pi/36#

and:

#(3pi)/4-9x= (3pi)/2=> x=-pi/18#

Graph of #f(x)=tan((3pi)/4-9x)#

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