Question

find the horizontal asymptotes of the rational function,
$f(x) = \frac{4x^2 - 1}{2x^2 + x - 6}$

select one:
a. $y = 0$
b. $y = \frac{1}{2}$
c. $y = 2$
d. no horizontal asymptote

Explanation:

Step1: Identify degree of numerator/denominator

Degree of numerator $4x^2-1$ is 2; degree of denominator $2x^2+x-6$ is 2.

Step2: Take ratio of leading coefficients

Leading coefficient of numerator is 4, leading coefficient of denominator is 2.
$\frac{4}{2}=2$

Answer:

C. $y = 2$