document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=295155>Question 295155</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the intercepts, asymptotes, use limits to describe the behavior at the vertical asymptotes and analyze and draw the graph of f(x)=(x+1)/(x^2-3x-10) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #212786 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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/cgi-bin/show-face.mpl?user=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=212786\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find the y-intercept, set x=0 and solve for y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=%280%2B1%29%2F%280%5E2-3%280%29-10%29=1%2F-10=-1%2F10 ALIGN=MIDDLE  ALT=\"f%280%29=%280%2B1%29%2F%280%5E2-3%280%29-10%29=1%2F-10=-1%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(0,-1/10)<BR>\n" );
document.write( "To find the x-intercept, set y=0 and solve for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=%28x%2B1%29%2F%28x%5E2-3x-10%29 ALIGN=MIDDLE  ALT=\"0=%28x%2B1%29%2F%28x%5E2-3x-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1=0 ALIGN=MIDDLE  ALT=\"x%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(-1,0)<BR>\n" );
document.write( "To find vertical asymptotes, look for x where the denominator goes to zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3x-10=0 ALIGN=MIDDLE  ALT=\"x%5E2-3x-10=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%28x-5%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%28x-5%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Two solutions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2=0 ALIGN=MIDDLE  ALT=\"x%2B2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-5=0 ALIGN=MIDDLE  ALT=\"x-5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To find horizontal asymptotes, divide all terms by the highest order of x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x%2Fx%5E2%2B1%2Fx%5E2%29%2F%28x%5E2%2Fx%5E2-3x%2Fx%5E2-10%2Fx%5E2%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%2Fx%5E2%2B1%2Fx%5E2%29%2F%28x%5E2%2Fx%5E2-3x%2Fx%5E2-10%2Fx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%281%2Fx%2B1%2Fx%5E2%29%2F%281-3%2Fx-10%2Fx%5E2%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%281%2Fx%2B1%2Fx%5E2%29%2F%281-3%2Fx-10%2Fx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now take the limit as x goes to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28+x-%3E-infinity%2C+f%28x%29+%29=%280%2B0%29%2F%281-0-0%29=0 ALIGN=MIDDLE  ALT=\"lim%28+x-%3E-infinity%2C+f%28x%29+%29=%280%2B0%29%2F%281-0-0%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "So there is a horizontal asymptote at y=0.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ". <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+300%2C+300%2C+-10%2C+10%2C+-2%2C+2%2C%0D%0Agreen%28line%28-2%2C-10%2C-2%2C10%29%29%2C%0D%0Agreen%28line%285%2C-10%2C5%2C10%29%29%2C%0D%0A%0D%0A+graph%28+300%2C+300%2C+-10%2C+10%2C+-2%2C+2%2C+%28x%2B1%29%2F%28x%5E2-3x-10%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );