# 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...
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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.

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.

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