Question

State the vertical asymptote of the rational function.. f(x) = quantity x minus six times quantity x plus six divided by quantity x squared minus nine.

Answer 1

The equation is f(x) =(x-6*(x+6))/(x^2 - 9).

For the vertical asymptote test in a rational function. The denominator is first set to zero.

x^2 - 9 = 0
x^2 = 9
x = +-3

The values for x are then substituted to the numerator.

x=3; x-6(x+6) = 3-6(3+6) = -51
x=-3; x-6(x+6) = -3-6(-3+6)= -21

The zeros of the denominator do not make the numerator zero so the vertical asymptotes are x= +-3