document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=985128>Question 985128</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #605968 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=605968\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 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.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "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. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );