Consider the function $F(x)=\frac{f(x)}{g(x)}$ with $g(a)=0.$ Does $F$ necessarily have a vertical asymptote at $x=$ a$?$ Explain your reasoning.

Choose the correct answer below.

A$.$ Yes. The function $F$ will always have a vertical asymptote at $x=$ a because $\underset{xa}{lim}F(x)=-$ whenever $g(a)=0.$

B$.$ No$.$ For example, if $f(x)=x1,g(x)=x^{2}2x1,$ and $a=-1,$ then the function $F$ does not have a vertical asymptote at $x=-1,$ even though $g(-1)=0.$

C$.$ 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 $g(2)=0.$

D$.$ Yes. The function $F$ will always have a vertical asymptote at $x=$a because $\underset{xa}{lim}F(x)-$ whenever $g(a)=0.$