y=3 tan x/4

Question

I neend help finding the asystoptote and solving the problem 

I have pre calculus

Answer 1

y = 3tan(x/4)

 

y = tanθ = sinθ/cosθ is undefined when cosθ = 0.  This occurs when    

θ = π/2 + kπ, where k = 0, ±1, ±2, ...

 

So, the graph of y = tanθ has vertical asymptotes at π/2 + kπ.

 

Therefore, the vertical asymptotes for y = 3tan(x/4) occur when               

    x/4 = π/2 + kπ

 

       x = 4(π/2 + kπ) = 2π + 4kπ

 

       x = 2π (for k = 0)

       x = 6π (for k = 1)

       x = -2π (for k = -1), etc

 

Vertical asymptotes:  x=2π, x=6π,x=10π,...

                              x=-2π, x=-6π, x=-10π, ...