Final answer:
The horizontal asymptote of the function f(x) = (-2x² + 3x + 6)/(x² + 1) is y = 0.
Step-by-step explanation:
The horizontal asymptote of the function f(x) = (-2x² + 3x + 6)/(x² + 1) can be found by observing the degrees of the numerator and denominator. Since the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. This means that as x approaches infinity or negative infinity, the function approaches 0.