Question 1047721
y=4 is horizontal asymptote.  The x^2 terms in numerator and denominator become increasingly more important to the extreme left and right.



Factorization makes {{{f(x)=((x-3)(4x+19))/((x+8)(x-3))}}}.  Only one of the denominator factors gives an asymtptote because the other is also in the numerator.  Hole at x=3, but ASYMPTOTE (vertical) at x=-8.