Which function's graph has asymptotes located at the values

Question

Which function's graph has asymptotes located at the values x=+/- n(pi)

 

1.) y=cscx

2) y=cosx

3)y=tanx

4)y=cotx

 

 

a) 1 only

B) 2 only

c) 1 and 3 only

d) 1 and 4 only

Answer 1

Hi

 

To have vertical asymptotes, the denominator of a function must equal 0. 

 

We know sin is 0 at Θ= 0, pi, 2pi, 3pi, 4pi........npi.  And at both + and -. 

 

Ok now let's look at the functions. 

 

csc x = 1/sin x

 

cos x = cos x and has no denominator

 

tan x = sin x /cos x

 

cot x = cos x / sin x

 

 

 

The only places where denominator can be 0 is csc x and cot x so D is your answer.