document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1153003>Question 1153003</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let f(x)= 3x^2+4x+1/3x^2+11x+6\r<BR>\n" );
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document.write( "This function has:\r<BR>\n" );
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document.write( "1) A y intercept at the point <BR>\n" );
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document.write( "Be sure to put your ordered pair in parentheses.\r<BR>\n" );
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document.write( "2) x intercepts at the point(s) <BR>\n" );
document.write( "  <BR>\n" );
document.write( "Be sure to put your ordered pair in parentheses.\r<BR>\n" );
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document.write( "3) Vertical asymptotes at x = <BR>\n" );
document.write( "  <BR>\n" );
document.write( "If there is more than one vertical intercept, separate the x-values with a comma.\r<BR>\n" );
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document.write( "4) Horizontal asymptote at y = <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #775149 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=775149\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=+%283x%5E2%2B4x%2B1%29%2F%283x%5E2%2B11x%2B6%29 ALIGN=MIDDLE  ALT=\"f%28x%29=+%283x%5E2%2B4x%2B1%29%2F%283x%5E2%2B11x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >............factor\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=+%283x%5E2%2B3x%2Bx%2B1%29%2F%283x%5E2%2B9x%2B3x%2B6%29+ ALIGN=MIDDLE  ALT=\"f%28x%29=+%283x%5E2%2B3x%2Bx%2B1%29%2F%283x%5E2%2B9x%2B3x%2B6%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=f%28x%29=+%28%283x%5E2%2B3x%29%2B%28x%2B1%29%29%2F%28%283x%5E2%2B9x%29%2B%282x%2B6%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=+%28%283x%5E2%2B3x%29%2B%28x%2B1%29%29%2F%28%283x%5E2%2B9x%29%2B%282x%2B6%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=f%28x%29=+%283x%28x%2B1%29%2B%28x%2B1%29%29%2F%283x%28x%2B3%29%2B2%28x%2B3%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=+%283x%28x%2B1%29%2B%28x%2B1%29%29%2F%283x%28x%2B3%29%2B2%28x%2B3%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=f%28x%29=+%28%283x%2B1%29%28x%2B1%29%29%2F%28%283x%2B2%29%28x%2B3%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=+%28%283x%2B1%29%28x%2B1%29%29%2F%28%283x%2B2%29%28x%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This function has:\r<BR>\n" );
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document.write( "1) A y intercept at the point: set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=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=f%28x%29=+%28%283%2A0%2B1%29%280%2B1%29%29%2F%28%283%2A0%2B2%29%280%2B3%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=+%28%283%2A0%2B1%29%280%2B1%29%29%2F%28%283%2A0%2B2%29%280%2B3%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=f%28x%29=+%281%2A1%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"f%28x%29=+%281%2A1%29%2F%282%2A3%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=f%28x%29=+1%2F6 ALIGN=MIDDLE  ALT=\"f%28x%29=+1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y intercept at the point: \r<BR>\n" );
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document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >) ->your ordered pair\r<BR>\n" );
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document.write( "2) x intercepts at the point(s) : set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=0 ALIGN=MIDDLE  ALT=\"f%28x%29=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=+%28%283x%2B1%29%28x%2B1%29%29%2F%28%283x%2B2%29%28x%2B3%29%29=0 ALIGN=MIDDLE  ALT=\"+%28%283x%2B1%29%28x%2B1%29%29%2F%28%283x%2B2%29%28x%2B3%29%29=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=+%28%283x%2B1%29%28x%2B1%29%29=0%2A%28%283x%2B2%29%28x%2B3%29%29 ALIGN=MIDDLE  ALT=\"+%28%283x%2B1%29%28x%2B1%29%29=0%2A%28%283x%2B2%29%28x%2B3%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=+%283x%2B1%29%28x%2B1%29=0 ALIGN=MIDDLE  ALT=\"+%283x%2B1%29%28x%2B1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%283x%2B1%29=0 ALIGN=MIDDLE  ALT=\"+%283x%2B1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=-1 ALIGN=MIDDLE  ALT=\"3x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1%2F3 ALIGN=MIDDLE  ALT=\"x=-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%2B1%29=0 ALIGN=MIDDLE  ALT=\"+%28x%2B1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><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;\" >\r<BR>\n" );
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document.write( "x intercepts at the point(s) : \r<BR>\n" );
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document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F3 ALIGN=MIDDLE  ALT=\"-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >),(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<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( "3) Vertical asymptotes at x => look for values that make denominator equal to zero\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=+%28%283x%2B1%29%28x%2B1%29%29%2F%28%283x%2B2%29%28x%2B3%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=+%28%283x%2B1%29%28x%2B1%29%29%2F%28%283x%2B2%29%28x%2B3%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=%283x%2B2%29%28x%2B3%29=0 ALIGN=MIDDLE  ALT=\"%283x%2B2%29%28x%2B3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, \r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%2B2%29=0 ALIGN=MIDDLE  ALT=\"%283x%2B2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=-2 ALIGN=MIDDLE  ALT=\"3x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2%2F3 ALIGN=MIDDLE  ALT=\"x=-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><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( "solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2%2F3 ALIGN=MIDDLE  ALT=\"x=-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <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( "4) Horizontal asymptote at y =\r<BR>\n" );
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document.write( "limit of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%5E2+%2B+4x+%2B+1%29%2F%283x%5E2+%2B+11+x+%2B+6%29-%3E1 ALIGN=MIDDLE  ALT=\"%283x%5E2+%2B+4x+%2B+1%29%2F%283x%5E2+%2B+11+x+%2B+6%29-%3E1\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> ± <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" );
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document.write( "to see images better, click on them\r<BR>\n" );
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document.write( " </SPAN>\n" );
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