Final answer:
The horizontal asymptote of the function s(x) = (3x² + 8x - 4)/(x² + 3) is y = 3, determined by the ratio of the leading coefficients of the numerator and the denominator.
Step-by-step explanation:
To identify the horizontal asymptote of the function s(x) = (3x² + 8x - 4)/(x² + 3), you need to compare the degrees of the numerator and the denominator polynomials.
Since the degrees of the numerator and the denominator are the same (both are degree 2), the horizontal asymptote is the ratio of the leading coefficients. Therefore, the horizontal asymptote of s(x) is y = 3/1, or simply, y = 3.