document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1158027>Question 1158027</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What function has the following characteristics?\r<BR>\n" );
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document.write( "A zero at x = 4 and at x = -2<BR>\n" );
document.write( "A y-intercept at y = 16/3<BR>\n" );
document.write( "A vertical asymptote at x = 3<BR>\n" );
document.write( "A slant asymptote at y = 2x + 2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #854546 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5385)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=854546\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Condition #1: A zero at x = 4 and at x = -2<BR>\n" );
document.write( "How to satisfy it: include(x-4) and (x+2) as factors<BR>\n" );
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document.write( "Condition #2: A y-intercept at y = 16/3<BR>\n" );
document.write( "How to satisfy it: after satisfying other conditions, add a constant factor K to satisfy <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=16%2F3 ALIGN=MIDDLE  ALT=\"f%280%29=16%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Condition #3: A vertical asymptote at x = 3<BR>\n" );
document.write( "How to satisfy it: include (x-3) as a denominator<BR>\n" );
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document.write( "Tentative solution to satisfy all 3 conditions above: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=K%28x-4%29%28x%2B2%29%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"f%28x%29=K%28x-4%29%28x%2B2%29%2F%28x-3%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%280%29=K%28-4%29%282%29%2F%28-3%29=K%288%2F3%29 ALIGN=MIDDLE  ALT=\"f%280%29=K%28-4%29%282%29%2F%28-3%29=K%288%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "to satisfy <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=16%2F3 ALIGN=MIDDLE  ALT=\"f%280%29=16%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > , we make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K%288%2F3%29=16%2F3 ALIGN=MIDDLE  ALT=\"K%288%2F3%29=16%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K=2 ALIGN=MIDDLE  ALT=\"K=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "So far, the function we have is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2%28x-4%29%28x%2B2%29%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"f%28x%29=2%28x-4%29%28x%2B2%29%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and its graph looks like this: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-16%2C12%2C-20%2C20%2C%0D%0Aline%283%2C-20%2C3%2C20%29%2Clocate%283.2%2C16%2Cx=3%29%2C%0D%0Agraph%28300%2C300%2C-16%2C12%2C-20%2C20%2C2%28x-4%29%28x%2B2%29%2F%28x-3%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Condition #4: A slant asymptote at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2x+%2B+2 ALIGN=MIDDLE  ALT=\"y+=+2x+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We need <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28x-%3Einfinity%2C%28f%28x%29-%282x%2B2%29%29%29=0 ALIGN=MIDDLE  ALT=\"lim%28x-%3Einfinity%2C%28f%28x%29-%282x%2B2%29%29%29=0\"   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-%282x%2B2%29=f%28x%29-2%28x%2B1%29 ALIGN=MIDDLE  ALT=\"f%28x%29-%282x%2B2%29=f%28x%29-2%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22=%22 ALIGN=MIDDLE  ALT=\"%22=%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x-4%29%28x%2B2%29%2F%28x-3%29-2%28x%2B1%29 ALIGN=MIDDLE  ALT=\"2%28x-4%29%28x%2B2%29%2F%28x-3%29-2%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22=%22 ALIGN=MIDDLE  ALT=\"%22=%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A2%28%28x-4%29%28x%2B2%29-%28x%2B1%29%28x-3%29%29%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"%0D%0A2%28%28x-4%29%28x%2B2%29-%28x%2B1%29%28x-3%29%29%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22=%22 ALIGN=MIDDLE  ALT=\"%22=%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%5E2-2x-8-%28x%5E2-2x-3%29%29%2F%28x-3%29%0D%0A ALIGN=MIDDLE  ALT=\"2%28x%5E2-2x-8-%28x%5E2-2x-3%29%29%2F%28x-3%29%0D%0A\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22=%22 ALIGN=MIDDLE  ALT=\"%22=%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%5E2-x%5E2-2x%2B2x-8%2B3%29%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"2%28x%5E2-x%5E2-2x%2B2x-8%2B3%29%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22=%22 ALIGN=MIDDLE  ALT=\"%22=%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28-5%29%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"2%28-5%29%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22=%22 ALIGN=MIDDLE  ALT=\"%22=%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"-10%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28x-%3Einfinity%2C%28f%28x%29-%282x%2B2%29%29%29=lim%28x-%3Einfinity%2C%28-10%2F%28x-3%29%29%29=0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );