Answer
Vertical asymptotes: $\qquad $ none.
Horizontal asymptote: $\qquad y=0$.
Work Step by Step
Use the procedure "Finding asymptotes of rational functions" on page 336.
1.
The denominator is zero for
$4x^{2}+1=0$
$4x^{2}=-1$
$x^{2}=-\displaystyle \frac{1}{4},\ \qquad $( no vertical asymptotes)
2.
The numerator has degree $n=1$,
the denominator has degree $m=2$
Since $n \lt m,\quad $the horizontal asymptote is $y=0.$
