Question

write the equation of the horizontal asymptote of the function: $y = \frac{3x^{2}+x - 2}{x^{2}+5x + 4}$

Explanation:

Step1: Determine degree of numerator and denominator

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

Step2: Find the horizontal - asymptote formula for equal - degree case

When $n = m$, the horizontal asymptote is given by $y=\frac{a_{n}}{b_{m}}$, where $a_{n}$ is the leading coefficient of the numerator and $b_{m}$ is the leading coefficient of the denominator. Here, $a_{n}=3$ and $b_{m}=1$.

Answer:

$y = 3$