document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=269456>Question 269456</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi. I am completely lost about this problem. Can you please explain how you get the answer. Thanks in advance \r<BR>\n" );
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document.write( "Find an equation of a rational function f that satisfies the conditions:<BR>\n" );
document.write( "vertical asymptotes: x = - 1, x = 6<BR>\n" );
document.write( "horizontal asymptote: y = 3<BR>\n" );
document.write( "x-intercepts: - 7, 5<BR>\n" );
document.write( "hole at x = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #197494 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=197494\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Lets go one step at a time.<BR>\n" );
document.write( "vertical asymptotes: x = - 1, x = 6<BR>\n" );
document.write( "we get a basic idea that our function is<BR>\n" );
document.write( "(i) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28ax%2Bb%29%2F%28%28x%2B1%29%28x-6%29%29 ALIGN=MIDDLE  ALT=\"y+=+%28ax%2Bb%29%2F%28%28x%2B1%29%28x-6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "horizontal asymptote: y = 3<BR>\n" );
document.write( "we know that as x approaches infinity, then the function approaches 3. SInce the denominator is degree 2, the numerator must be degree 2, so we could say<BR>\n" );
document.write( "(ii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%283x%5E2%2B+ax%2Bb%29%2F%28%28x%2B1%29%28x-6%29%29 ALIGN=MIDDLE  ALT=\"y+=+%283x%5E2%2B+ax%2Bb%29%2F%28%28x%2B1%29%28x-6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "x-intercepts: - 7, 5<BR>\n" );
document.write( "If we let x = -7 or x = 5, then the function should become 0.<BR>\n" );
document.write( "part 1 - x = -7 gets us<BR>\n" );
document.write( "(iii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%283%28-7%29%5E2+-+7a+%2B+b%29%2F%28%28%28-7%29%2B1%29%28%28-7%29-6%29%29 ALIGN=MIDDLE  ALT=\"y+=+%283%28-7%29%5E2+-+7a+%2B+b%29%2F%28%28%28-7%29%2B1%29%28%28-7%29-6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( "(iv) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28147+-+7a+%2B+b%29%2F78 ALIGN=MIDDLE  ALT=\"y+=+%28147+-+7a+%2B+b%29%2F78\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this means that the numerator = 0, so<BR>\n" );
document.write( "If a = 6, then b = -105. So our equation is now<BR>\n" );
document.write( "(v) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%283x%5E2%2B+6x+-+105%29%2F%28%28x%2B1%29%28x-6%29%29 ALIGN=MIDDLE  ALT=\"y+=+%283x%5E2%2B+6x+-+105%29%2F%28%28x%2B1%29%28x-6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "part 2 - x = 5 gets us<BR>\n" );
document.write( "(vi) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%283%2A5%5E2%2B+5a+%2B+b%29%2F%28%285%2B1%29%285-6%29%29 ALIGN=MIDDLE  ALT=\"y+=+%283%2A5%5E2%2B+5a+%2B+b%29%2F%28%285%2B1%29%285-6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( "(vii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%2875%2B+5a+%2B+b%29%2F%28-6%29 ALIGN=MIDDLE  ALT=\"y+=+%2875%2B+5a+%2B+b%29%2F%28-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this means that the numerator = 0, so<BR>\n" );
document.write( "If a = 6, then b = -105. The key part is setting the numerator of (iv) = numerator of (vii) to get values for a and b that work<BR>\n" );
document.write( "So, our new equation is<BR>\n" );
document.write( "(viii) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%283x%5E2%2B+6x+-+105%29%2F%28%28x%2B1%29%28x-6%29%29 ALIGN=MIDDLE  ALT=\"y+=+%283x%5E2%2B+6x+-+105%29%2F%28%28x%2B1%29%28x-6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "hole at x = 0 <BR>\n" );
document.write( "this means that we multiply both numerator and denominator by x to get our final answer equation as<BR>\n" );
document.write( "(ix) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28%28x%29%283x%5E2%2B+6x+-+105%29%29%2F%28%28x%29%28x%2B1%29%28x-6%29%29 ALIGN=MIDDLE  ALT=\"y+=+%28%28x%29%283x%5E2%2B+6x+-+105%29%29%2F%28%28x%29%28x%2B1%29%28x-6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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