Question

write the equation of all horizontal asymptotes of the function $f(x)=\frac{5x^{2}-6x^{3}}{0x^{3}+6x^{3}}$. answer attempt 1 out of 3 one horizontal asymptote

Explanation:

Step1: Identify the degrees of numerator and denominator

The numerator of $f(x)=\frac{5x^{2}-6x^{3}}{0x^{3}+6x^{3}}$ has degree 3 (highest - power of $x$ is 3), and the denominator has degree 3.

Step2: Find the horizontal asymptote

For a rational function $\frac{a_nx^n+\cdots+a_0}{b_mx^m+\cdots + b_0}$ where $n = m$, the horizontal asymptote is $y=\frac{a_n}{b_m}$. Here, $a_n=-6$ (coefficient of $x^3$ in the numerator) and $b_m = 6$ (coefficient of $x^3$ in the denominator). So, $y=\frac{-6}{6}=-1$.

Answer:

$y = - 1$