Question

what is the horizontal asymptote of the following rational function?
$f(x) = \frac{4x-1}{2x^2+5}$
$\bigcirc \\ y=0$
$\bigcirc \\ y=\frac{1}{2}$
$\bigcirc \\ y=2$
$\bigcirc \\ $there is no horizontal asymptote

Explanation:

Step1: Identify degrees of numerator/denominator

The numerator $4x-1$ has degree 1; the denominator $2x^2+5$ has degree 2.

Step2: Apply horizontal asymptote rule

When denominator degree > numerator degree, the horizontal asymptote is $y=0$.

Answer:

$y=0$