Find the horizontal asymptote of \( f(x)=\frac{4 x^{3}-x-3}{-5 x^{3}-4 x^{2}+1} \) \( y=\square \)

To find the horizontal asymptote of the function \( f(x) = \frac{4x^3 - x - 3}{-5x^3 - 4x^2 + 1} \), we look at the degrees of the polynomials in the numerator and the denominator. Both the numerator and the denominator are of degree 3. When the degrees are equal, the horizontal asymptote is found by taking the ratio of the leading coefficients. The leading coefficient of the numerator (4) divided by the leading coefficient of the denominator (-5) gives us: \[ y = \frac{4}{-5} = -\frac{4}{5} \] Therefore, the horizontal asymptote is \( y = -\frac{4}{5} \).