Answer
vertical asymptotes: $x=2$ and $x=-1.75$
horizontal asymptote: $y=0.5$
Work Step by Step
Vertical asymptotes occur where the denominator is zero. Thus, we set the denominator to zero and solve for the $x$ values to find the vertical asymptotes:
$(x-2)(4x+7)=0$
$x=2$ and $x=-1.75$
Thus the vertical asymptotes are $x=2$ and $x=-1.75$
Here, the degrees of the numerator and the denominator are the same. Thus, the horizontal asymptote is the quotient of the leading coefficients:
$y=\frac{2}{4}=0.5$
