document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=65116>Question 65116</A>: <I><SPAN STYLE=\"word-break: break-all;\"> graph\r<BR>\n" );
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document.write( "F(x) = x-2 there is a line under x-2<BR>\n" );
document.write( "       x+4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #45699 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=45699\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> graph<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F%28x%29=%28x-2%29%2F%28x%2B4%29 ALIGN=MIDDLE  ALT=\"F%28x%29=%28x-2%29%2F%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Because the leading terms in the denominator and numerator have the same degree and coefficients, there is a horizontal asymptote of y=1/1=1.  I usually draw a faint dashed line for the asymptotes, because your graph can't equal that.<BR>\n" );
document.write( "There is a vertical asymptote where the rational function is undefined (where the denominator=0).<BR>\n" );
document.write( "The vertical asymptote is:<BR>\n" );
document.write( "x+4=0<BR>\n" );
document.write( "x+4-4=0-4<BR>\n" );
document.write( "x=-4  Draw a faint dashed line there (unfortunatley this program is going to draw a solid dashed line there.)<BR>\n" );
document.write( "Pick two numbers on both sides of the asymptote to plot.<BR>\n" );
document.write( "If x=-8<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-8%29=%28-8-2%29%2F%28-8%2B4%29 ALIGN=MIDDLE  ALT=\"f%28-8%29=%28-8-2%29%2F%28-8%2B4%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%28-8%29=-10%2F%28-4%29 ALIGN=MIDDLE  ALT=\"f%28-8%29=-10%2F%28-4%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%28-8%29=5%2F2 ALIGN=MIDDLE  ALT=\"f%28-8%29=5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or 2.5<BR>\n" );
document.write( "Plot (-8,5/2)<BR>\n" );
document.write( "If x=-6<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-6%29=%28-6-2%29%2F%28-6%2B4%29 ALIGN=MIDDLE  ALT=\"f%28-6%29=%28-6-2%29%2F%28-6%2B4%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%28-6%29=-8%2F%28-2%29 ALIGN=MIDDLE  ALT=\"f%28-6%29=-8%2F%28-2%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%28-6%29=4 ALIGN=MIDDLE  ALT=\"f%28-6%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Plot (-6,4)<BR>\n" );
document.write( "If x=-2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-2%29=%28-2-2%29%2F%28-2%2B4%29 ALIGN=MIDDLE  ALT=\"f%28-2%29=%28-2-2%29%2F%28-2%2B4%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%28-2%29=-4%2F2 ALIGN=MIDDLE  ALT=\"f%28-2%29=-4%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-2%29=-2 ALIGN=MIDDLE  ALT=\"f%28-2%29=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Plot (-2,-2)<BR>\n" );
document.write( "If x=0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=%280-2%29%2F%280%2B4%29 ALIGN=MIDDLE  ALT=\"f%280%29=%280-2%29%2F%280%2B4%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=-2%2F4 ALIGN=MIDDLE  ALT=\"f%280%29=-2%2F4\"   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=-1%2F2 ALIGN=MIDDLE  ALT=\"f%280%29=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Plot (0,-1/2)<BR>\n" );
document.write( "This equation has an x-intercept when the numerator=0.<BR>\n" );
document.write( "x-2=0<BR>\n" );
document.write( "x-2+2=0+2<BR>\n" );
document.write( "x=2  Plot (2,0)<BR>\n" );
document.write( "After you connect the points remembering not to cross the asymptotes you get this:  Note this program draws in the vertical asymptote x=-4, it is not part of the graph.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C%28x-2%29%2F%28x%2B4%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C%28x-2%29%2F%28x%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Happy Calculating!!! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );