To find the horizontal asymptote of the given function, we need to compare the degrees of the numerator and denominator.
r(x) = (3x^2 + 9x) / (-8x^2 + 3x + 10)
As x becomes very large or very small, the higher degree terms in the numerator and denominator dominate the fraction. Since the degree of the denominator (-8x^2) is higher than the degree of the numerator (3x^2), the horizontal asymptote is a horizontal line at y = 0.
Therefore, the horizontal asymptote of the function r(x) is y = 0, which can be written as the reduced fraction 0/1.