Final answer:
To find the vertical asymptotes of f(x) = -(8x²)/(9-x²), set the denominator equal to zero; the solutions x=3 and x=-3 are the vertical asymptotes. The function has a horizontal asymptote at y=0, as the degrees of the numerator and denominator are equal.
Step-by-step explanation:
The student is asking how to find any horizontal or vertical asymptotes for the function f(x) = - (8x²)/(9-x²). First, to find vertical asymptotes, we set the denominator equal to zero and solve for x. So, for the equation 9-x² = 0, the solutions are x = 3 and x = -3, which are our vertical asymptotes.
To find horizontal asymptotes, we compare the degrees of the numerator and the denominator. Since the degree of the numerator (2) is less than the degree of the denominator (2), we know the function has a horizontal asymptote at y = 0.