document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=912267>Question 912267</A>: <I><SPAN STYLE=\"word-break: break-all;\"> x- and y intercept and horizontal and vertical asymptotes of this rational function:\r<BR>\n" );
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document.write( "y = (1/6)(x+2)^3(x-1)^2(6-x)\r<BR>\n" );
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document.write( "I think the x intercepts must be (-2,0)(+1,0) and (+6,0)\r<BR>\n" );
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document.write( "I understand there is no asymptotes but is there a y-intercept? and how would I go about graphing such a function?\r<BR>\n" );
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document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #553701 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=553701\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Polynomial equation in factored form.<BR>\n" );
document.write( "x-intercepts are readable directly from the factors:  -2, 1, 6.<BR>\n" );
document.write( "y-intercept is y where x=0.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F6%29%282%5E3%29%28-1%29%5E2%286%29 ALIGN=MIDDLE  ALT=\"y=%281%2F6%29%282%5E3%29%28-1%29%5E2%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=8 ALIGN=MIDDLE  ALT=\"y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Do no confuse polynomial functions with rational functions!  You say you understand that the equation has no asymptotes.  A polynomial function is defined for all x values and is continuous everywhere.  A rational function will have an expression of x in the denominator, and this causes some effect (in some cases) on sign of the function and also forces either a missing value for y or a vertical asymptote.\r<BR>\n" );
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document.write( "How to Graph:<BR>\n" );
document.write( "The roots or x-intercepts make specific intervals on the x-axis.  The graph will either touch or cross the x axis at the roots.  Check the sign of y for each interval to know if that interval has positive y values or negative y values; and this helps you to sketch the graph.\r<BR>\n" );
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document.write( "Something is wrong with this graph....<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-6%2C7%2C-10%2C10%2C%281%2F6%29%28x%2B2%29%5E3%28x-1%29%5E2%286-x%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-6%2C7%2C-10%2C10%2C%281%2F6%29%28x%2B2%29%5E3%28x-1%29%5E2%286-x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The graph seems to be displaying wrongly. </SPAN>\n" );
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