Question

write the equation of all horizontal asymptotes of the function $f(x)=\frac{3x^{2}+2x^{4}}{5x + 2x^{4}}$. answer attempt 1 out of 2 one horizontal asymptote

Explanation:

Step1: Identify the degrees of numerator and denominator

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

Step2: Find the horizontal asymptote

When $n = m$, the horizontal asymptote is given by the ratio of the leading - coefficients. The leading coefficient of the numerator is $a = 2$ and the leading coefficient of the denominator is $b = 2$. So, $y=\frac{a}{b}$.
$y=\frac{2}{2}=1$

Answer:

$y = 1$