Question

Show all work to identify the asymptotes and zero of the function f of x equals 3 x over quantity x squared minus 9.

Answer 1

f(x) = 3x/(x^2-9)

factoring the denominator:

f(x) = 3x/(x+3)(x-3)

the function is undefined when the denominator equals 0, so (x+3) = 0 and (x-3) = 0, giving us x = -3 and x = 3 as vertical asymptotes

going back to the original polynomial, the degree on x is larger in the denominator than in the numerator, so you also have a horizontal asymptote at y = 0