The horizontal asymptote is y = -3.
How to identify horizontal asymptote of a function.
To identify the horizontal asymptotes of the function p(x) = (-3x² + 4x - 1)/(x² + 1), we need to compare the degrees of the numerator and denominator polynomials.
The degree of the numerator is 2 and the degree of the denominator is also 2. Since the degrees are the same, let's look at the leading coefficients. The leading coefficient of the numerator is -3, and for the denominator, it's 1.
Since the degrees are equal, the horizontal asymptote is given by the ratio of the leading coefficients, which is -3/1 = -3
Therefore, the horizontal asymptote is y = -3.