Consider the function F(x) = 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. No. For example, if f(x) = x + 1, g(x) = x² + 2x + 1, and a = -1, then the function F does not have a vertical asymptote at x = -1, even though g(-1)=0.
B. Yes. The function F will always have a vertical asymptote at x = a because lim F(x)+ + whenever g(a) = 0. Xa
C. No. For example, if f(x) = x² - 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 lim F(x) = 100 whenever g(a) = 0. Xa
