find the equation of the horizontal asymptote of the function f(x)=x²/(x⁵ + 7).\no y = 0\no f(x) has no…

Explanation:

Step1: Recall horizontal - asymptote rules

For a rational function $f(x)=\frac{a_nx^n+\cdots+a_0}{b_mx^m+\cdots + b_0}$, we consider the degrees of the numerator $n$ and denominator $m$. Here, $n = 2$ (degree of $x^2$) and $m = 5$ (degree of $x^5+7$).

Step2: Apply the rule for $n<m$

When $n < m$, the horizontal asymptote is $y = 0$. Since $2<5$ for the function $f(x)=\frac{x^2}{x^5 + 7}$, the horizontal asymptote is $y = 0$.

Answer:

A. $y = 0$