Question

Which is an asymptote of the graph of the function y=tan(3/4x)?

Answer 1

ANSWER

$x = - \frac{2\pi}{3}$

EXPLANATION

The given function has equation

$y = \tan( \frac{3}{4}x)$

This can be rewritten as

$y = \frac{ \sin( \frac{3}{4}x ) } { \cos(\frac{3}{4}x )}$

The asymptote occurs at:

$\cos(\frac{3}{4}x ) = 0$

This implies that,

$\frac{3}{4} x = \frac{ \pi}{2}$

$x = \frac{ \pi}{2} \times \frac{4}{3}$

$x = \frac{2\pi}{3}$

Or

$\frac{3}{4} x = - \frac{ \pi}{2}$

$x = \frac{ - \pi}{2} \times \frac{4}{3}$

$x = - \frac{2\pi}{3}$

The second choice is correct.

Answer 2

Answer:

B) $x = \frac{2\pi }{3}$

Step-by-step explanation:

this is the correct answer on ed-genuity, hope this helps! :)