document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1160127>Question 1160127</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write an equation for a rational function with:\r<BR>\n" );
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document.write( "Vertical asymptotes at x = -6 and x = -4\r<BR>\n" );
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document.write( "x intercepts at x = -1 and x = -3\r<BR>\n" );
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document.write( "Horizontal asymptote at y = 7 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #783286 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=783286\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Write an equation for a rational function with:<BR>\n" );
document.write( "Vertical asymptotes at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-6 ALIGN=MIDDLE  ALT=\"x+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-4 ALIGN=MIDDLE  ALT=\"x+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x intercepts at<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;\" > and<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+-3 ALIGN=MIDDLE  ALT=\"+x+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Horizontal asymptote at<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+7 ALIGN=MIDDLE  ALT=\"+y+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a rational function: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=p%28x%29%2Fq%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29=p%28x%29%2Fq%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "given:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > intercepts at <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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3 ALIGN=MIDDLE  ALT=\"x+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " the x -intercepts exist when the numerator is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29=%28x-%28-1%29%29%28x-%28-3%29%29 ALIGN=MIDDLE  ALT=\"p%28x%29=%28x-%28-1%29%29%28x-%28-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29=%28x%2B1%29%28x%2B3%29 ALIGN=MIDDLE  ALT=\"p%28x%29=%28x%2B1%29%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29=x%5E2+%2B+4+x+%2B+3 ALIGN=MIDDLE  ALT=\"p%28x%29=x%5E2+%2B+4+x+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To find the vertical asymptote(s) of a rational function, simply set the denominator equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "you are given vertical asymptotes at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-6 ALIGN=MIDDLE  ALT=\"x+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-4 ALIGN=MIDDLE  ALT=\"x+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so denominator is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%28x%29=%28x-%28-6%29%29%28x-%28-4%29%29 ALIGN=MIDDLE  ALT=\"q%28x%29=%28x-%28-6%29%29%28x-%28-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%28x%29=%28x%2B6%29%28x%2B4%29 ALIGN=MIDDLE  ALT=\"q%28x%29=%28x%2B6%29%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%28x%29=x%5E2+%2B+10+x+%2B+24 ALIGN=MIDDLE  ALT=\"q%28x%29=x%5E2+%2B+10+x+%2B+24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so far <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x%5E2+%2B+4+x+%2B+3%29%2F%28x%5E2+%2B+10+x+%2B+24%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%5E2+%2B+4+x+%2B+3%29%2F%28x%5E2+%2B+10+x+%2B+24%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you are given horizontal asymptote at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+7 ALIGN=MIDDLE  ALT=\"y+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and then the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is the ratio of the leading coefficients \r<BR>\n" );
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document.write( "so, your function is\r<BR>\n" );
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document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%287x%5E2+%2B+28x+%2B+21%29%2F%28x%5E2+%2B+10+x+%2B+24%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%287x%5E2+%2B+28x+%2B+21%29%2F%28x%5E2+%2B+10+x+%2B+24%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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