Question

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

1)x=-4pi/3
2)x=-2pi/3
3)x=3pi/4
4)x=3pi/2

Answer is 2

Answer 1

B)
`x = (2\pi )/(3)`

Explanation:

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

Answer 2

`x = - (2\pi)/(3)`

EXPLANATION

The given function has equation

`y = \tan( (3)/(4)x)`

This can be rewritten as

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

The asymptote occurs at:

`\cos((3)/(4)x ) = 0`

This implies that,

`(3)/(4) x = ( \pi)/(2)`

`x = ( \pi)/(2) * (4)/(3)`

`x = (2\pi)/(3)`

Or

`(3)/(4) x = - ( \pi)/(2)`

`x = ( - \pi)/(2) * (4)/(3)`

`x = - (2\pi)/(3)`

The second choice is correct.