ANSWER
[tex]x = - \frac{2\pi}{3} [/tex]
EXPLANATION
The given function has equation
[tex]y = \tan( \frac{3}{4}x) [/tex]
This can be rewritten as
[tex]y = \frac{ \sin( \frac{3}{4}x ) } { \cos(\frac{3}{4}x )}[/tex]
The asymptote occurs at:
[tex]\cos(\frac{3}{4}x ) = 0[/tex]
This implies that,
[tex] \frac{3}{4} x = \frac{ \pi}{2} [/tex]
[tex]x = \frac{ \pi}{2} \times \frac{4}{3} [/tex]
[tex]x = \frac{2\pi}{3} [/tex]
Or
[tex]\frac{3}{4} x = - \frac{ \pi}{2} [/tex]
[tex]x = \frac{ - \pi}{2} \times \frac{4}{3} [/tex]
[tex]x = - \frac{2\pi}{3} [/tex]
The second choice is correct.
