Question 985128: How do you determine the range of a bottom-heavy rational function? The function I need to find the range of is y=(-2x+2)/((x^2)+2x). I know that the horizontal asymptote is y=0. The range includes y=0, because when x=1 then y=0. In the graph, there is a gap between the top and bottom sections.This means that there is a gap in the range. How do I figure out where this gap starts and ends (how can I accurately determine the range of this function)?
Answer by josgarithmetic(39618)   (Show Source):
You can put this solution on YOUR website! 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.
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