1. find the horizontal asymptote(s). f(x) = (4x² + x - 9)/(2x² - 6x + 1) y = -4 y = -2 y = 4 y = 2
1. find the horizontal asymptote(s). f(x) = (4x² + x - 9)/(2x² - 6x + 1) y = -4 y = -2 y = 4 y = 2
Answer
Explanation:
Step1: Identify degree of polynomials
The degree of the numerator $4x^{2}+x - 9$ and the denominator $2x^{2}-6x + 1$ is $n = m=2$.
Step2: Use horizontal - asymptote rule
When $n = m$, the horizontal asymptote is $y=\frac{a_{n}}{b_{m}}$, where $a_{n}$ is the leading coefficient of the numerator and $b_{m}$ is the leading coefficient of the denominator. Here $a_{n}=4$ and $b_{m}=2$. So $y=\frac{4}{2}=2$.
Answer:
$y = 2$