Question 985128
I made an attempt to study your equation, and it may have  a gap in y between the horizontal asymptote and some other value.  How is your skill with Calculus and Derivatives?   First-derivative may give information about local maximum or local minimum.  Otherwise, around critical x  near -2, y extends toward plus and minus infinities, depending on which side of x=-2.


This question about range would seem a better exercise in Calculus than in College Algebra.  Find the first derivative, set equal to zero, and identify local minimum or maximum.