document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164742>Question 1164742</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let f be the function defined by f(x)=(cx-(5x^2))/((2x^2)+ax+b), where a, b, and c are constants. The graph of f has a vertical asymptotes at x=1, and f has a removable discontinuity at x=-2. \r<BR>\n" );
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document.write( "a) show that a=2 and b=-4<BR>\n" );
document.write( "b) find the value of c, justify your answer. <BR>\n" );
document.write( "d) Write an equation for the horizontal asymptote to the graph of f. Please show work. <BR>\n" );
document.write( "c) In order to make f continuous at x=-2, f(-2) should be defined as what? Justify the answer\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 #789156 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=789156\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "If f has a vertical asymptote at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ 1\"> then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ -\ 1\"> must be a factor of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2x^2\ +\ ax\ +\ b\"> and if f has a removable discontinuity at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ -2\"> then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ +\ 2\"> must be a factor of both the numerator and the denominator functions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (x\ -\ 1)(x\ +\ 2)\ =\ x^2\ +\ x\ -\ 2\">\r<BR>\n" );
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document.write( "So we need another factor of 2 for the denominator so the denominator function is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2x^2\ +\ 2x\ -\ 4\">\r<BR>\n" );
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document.write( "Demonstrating that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\ =\ 2\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\ =\ -4\">\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ +\ 2\"> is also a factor of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large cx\ -\ 5x^2\">, if you factor <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -5x\"> from the numerator function you get <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -5x(-\frac{c}{5}\ +\ x)\">, so <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -\frac{c}{5}\ +\ x\ =\ x\ +\ 2\"> means that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large c\ =\ -10\">\r<BR>\n" );
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document.write( "The lead coefficient of the numerator is -5 and the lead coefficient of the denominator is 2, therefore the equation of the horizontal asymptote is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\ =\ -\frac{5}{2}\">\r<BR>\n" );
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document.write( "For the last part, remove the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ +\ 2\"> factor from both the numerator and denominator and then evaluate at -2\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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