# Consider the function F(x)= f(x)/g(x) with ​g(a)equals=0. Does F necessarily have a vertical asymptote at x equals=​a?

Choose the correct answer below. A. Yes. The function F will always have a vertical asymptote at x=a because limx right arrow a of F(x)= plus or minus infinity limx→a F(x)=±∞ whenever ​g(a)=0. B. Yes. The function F will always have a vertical asymptote at x=a because limx right F(x) does not equal plus or minus... show more Choose the correct answer below.
A.
Yes. The function F will always have a vertical asymptote at x=a because limx right arrow a of F(x)= plus or minus infinity limx→a F(x)=±∞ whenever ​g(a)=0.
B.
Yes. The function F will always have a vertical asymptote at x=a because limx right F(x) does not equal plus or minus infinity limx→a F(x)≠±∞ whenever ​g(a)=0.
C.
No. For​ example, if ​f(x)=xplus+​1, ​g(x)equals=x^2+2x+​1, and a=−​1, then the function F does not have a vertical asymptote at x =−​1, even though ​g(−​1)=0.
D.
No. For​ example, if ​f(x)=x^2−​4, ​g(x)=x−​2, and a=​2, then the function F does not have a vertical asymptote at x=​2, even though ​g(2)=0.