The vertical asymptote of a trig function: which is *not* an asymptote of 1/sinpix?

[vanyaa]

Which of the following is not a vertical asymptote of f(x)=1/sinπx?​

a) x=1​

b) x=0​

C) x= -2​

D) x= 1/2​

I have been struggling to understand this question for the past 30 minutes can someone please help me

 

[stapel]

Which of the following is not a vertical asymptote of f(x) = 1/sinpix?

a) x = 1
b) x = 0
c) x = -2
d) x = 1/2

I have been struggling to understand this question for the past 30 minutes can someone please help me

Okay; in the first five minutes, you drew the graph. In the following five minutes, you compared the graph's asymptotes to the listed answer options. And... then what?

Please be complete. Thank you!

 

[Bruce]

Vertical asymptotes occur at values of x that cause the function's denominator to become zero.

 

[Dr.Peterson]

Which of the following is not a vertical asymptote of f(x)=1/sinπx?

a) x=1​

b) x=0​

C) x= -2​

D) x= 1/2​

I have been struggling to understand this question for the past 30 minutes can someone please help me

What did you get when you tried each of the four given values of x in the function?

In order to help, we need to see what your struggles looked like! If you mean literally that you couldn't understand what the question is asking, tell us what you understand a vertical asymptote to be, and what it would take for a vertical line not to be a vertical asymptote.

 

[Steven G]

Vertical asymptotes occur at values of x that cause the function's denominator to become zero.

No, that is NOT true. I am surprised and disappointed that helpers here gave you the sums up on your post.
A vertical asymptote occurs at values of x that cause the function's denominator to become zero PROVIDED this x values does not cause the numerator to be zero as well.

 

[Dr.Peterson]

No, that is NOT true. I am surprised and disappointed that helpers here gave you the sums up on your post.
A vertical asymptote occurs at values of x that cause the function's denominator to become zero PROVIDED this x values does not cause the numerator to be zero as well.

Actually, what he said is true, because he referred not to "any" function, but to "the" [given] function, whose numerator, 1, is never zero.

But what are "sums up"?