find the horizontal asymptote of f(x) = (4x - 4x^3 + 5)/(-3x^3 - x^2 + 3). y = question help: video message…

Explanation:

Step1: Identify the degrees of polynomials

The degree of the numerator $4x - 4x^{3}+5$ is $n = 3$ (highest - power of $x$), and the degree of the denominator $-3x^{3}-x^{2}+3$ is $m = 3$.

Step2: Use the horizontal - asymptote rule for equal degrees

When $n = m$, the horizontal asymptote $y$ is given by the ratio of the leading coefficients. The leading coefficient of the numerator is $a=-4$ and the leading coefficient of the denominator is $b = - 3$. The formula for the horizontal asymptote is $y=\frac{a}{b}$. So, $y=\frac{-4}{-3}=\frac{4}{3}$.

Answer:

$y = \frac{4}{3}$