Question

Which two equations are the equations of vertical asymptotes of the function y = 5∕3 tan(3∕4x)?

A) x-2pi/3 and x=-2pi/3
B) x=0 and x=2pi/3
C) x=4pi/3 and x =4pi/3
D) x=0 and x=4pi/3

I did not know how to paste the pi symbol so I used the letters (pi)

Answer 1

A

Explanation:

Answer 2

A)x=2pi/3 and x=-2pi/3

Explanation:

The function
`y=(5)/(3)tan((3)/(4)x)` has vertical asymptotes in the values where the tan(a) has vertical asymptotes.

we know that tan(a) has vertical asymptotes in
`a=(\pi )/(2)` and
`a=(-\pi )/(2)`, if we made
`a=(3x)/(4)` and solve for x, we get:

for
`a=(\pi )/(2)`

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

for
`a=(-\pi )/(2)`

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

Finally, the function
`y=(5)/(3)tan((3)/(4)x)` has vertical asymptotes in the values x=2pi/3 and x=-2pi/3