Which function's graph has asymptotes located at the values π/2±nπ? (if you can't read it it's pi/2 +- npi i - y = sec x ii - y = cos x iii - y = tan x iv - y = cot x

Step-by-step explanation:

First, let's understand what the asymptotes are. The asymptotes are straight lines to which the function approaches indefinitely, when at least one of the variables (x or y) tends to infinity. Generally, rational functions have asymptotic behavior. Now, let's check the functions:

This function will have asymptotes at the points where:

Because we can't divide by 0. Now, cos(x)=0 at π/2, 3π/2, 5π/2, 7π/2, and so on... in other terms:

So, this function is a correct answer

is is continuous throughout its domain, so it doesn't have asymptotes.

Similarly as with sec(x), This function also will have asymptotes at the points where:

so, this function is a correct answer as well.

This function will have asymptotes at the points where:

sin(x)=0 at 0, π, 2π, 3π, and so on... in other terms:

Therefore, this function isn´t a correct answer.

I attached the graphics where you can see that the answers are correct

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional

idk

step-by-step explanation: