find all horizontal asymptotes of the following function. f(x) = (3x - 15)/(6x^2 - 22x - 40)
find all horizontal asymptotes of the following function. f(x) = (3x - 15)/(6x^2 - 22x - 40)
Answer
Explanation:
Step1: Determine the degrees of numerator and denominator
The degree of the numerator $3x - 15$ is $n = 1$ (highest - power of $x$ is 1), and the degree of the denominator $6x^{2}-22x - 40$ is $m = 2$ (highest - power of $x$ is 2).
Step2: Apply the horizontal - asymptote rule
When $n\lt m$, the horizontal asymptote is $y = 0$. Since $1\lt2$, as $x\to\pm\infty$, the value of $y = f(x)\to0$.
Answer:
$y = 0$