Question

determine the equation of the horizontal asymptote, if any, of the function below. $f(x)=\frac{2x^{2}+10x + 8}{x^{2}-8x - 15}$ equation of horizontal asymptote: blank no horizontal asymptote exists. question help: video message instructor submit question

Explanation:

Step1: Identify degrees of numerator and denominator

The degree of the numerator $2x^{2}+10x + 8$ is $n = 2$ (highest - power of $x$), and the degree of the denominator $x^{2}-8x - 15$ is $m=2$.

Step2: Find the horizontal - asymptote formula

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, $a_{n}=2$ and $b_{m}=1$.

Step3: Calculate the horizontal - asymptote

$y=\frac{2}{1}=2$.

Answer:

$y = 2$