document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=916902>Question 916902</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Understanding why the graph looks the way it does:\r<BR>\n" );
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document.write( "f(x) = (4(x-5))/((x+2)(10-x))\r<BR>\n" );
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document.write( "I understand how to find the vertical/horizontal asymptotes and x and y intercept and I understand the middle line going through the middle of the graph but the other two lines curving along the asymptotes why are they there and how do I predict them and know when/where to plot them when I graph on paper? why are they in those positions and why not others?\r<BR>\n" );
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document.write( "http://i.imgur.com/Fkl11xT.png\r<BR>\n" );
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document.write( "Thank you<BR>\n" );
document.write( "Please explain </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #556387 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=556387\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Understanding why the graph looks the way it does: <BR>\n" );
document.write( "f(x) = (4(x-5))/((x+2)(10-x)) <BR>\n" );
document.write( "I understand how to find the vertical/horizontal asymptotes and x and y intercept and I understand the middle line going through the middle of the graph but the other two lines curving along the asymptotes why are they there and how do I predict them and know when/where to plot them when I graph on paper? why are they in those positions and why not others?<BR>\n" );
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document.write( "Vertical asymptotes at x = -2 and x = 10<BR>\n" );
document.write( "Horizontal asymptote at y = x/x^2 = 0/1 = 0<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "End Behavior depends on y = x/(-x^2) = -1/x<BR>\n" );
document.write( "As x goes to -oo y goes to +0 (above the x-axis)<BR>\n" );
document.write( "As x goes to +oo y goes to -0 (below the x-axis)<BR>\n" );
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document.write( "Sketching the curve from the left to the right::<BR>\n" );
document.write( "Start near zero above the x-axis<BR>\n" );
document.write( "Curve up to a VA at x = -2<BR>\n" );
document.write( "Signs switch from y positive to y negative  at x = -2<BR>\n" );
document.write( "------<BR>\n" );
document.write( "Curve up from the VA asymptote to intersect at (5,0)<BR>\n" );
document.write( "Continue up to VA asymptote at x = 10<BR>\n" );
document.write( "Signs switch at (x = 10)<BR>\n" );
document.write( "Curve up from the VA asymptote to HA (y = 0) below the x-axis.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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document.write( " </SPAN>\n" );
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