document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1169077>Question 1169077</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am rational function having a vertical asymptote at the lines x=3 x=-3, and a horizontal asymptote at y=1. If only my x-intercept is 5 and my y-interxepr is 5/9, who am I?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #793724 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=793724\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Vertical asymptotes at x=3 and x=-3 --> factors of (x+3) and (x-3) in the denominator:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+a%2F%28%28x%2B3%29%28x-3%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+a%2F%28%28x%2B3%29%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Only x-intercept at x=5 --> only linear factors in the numerator are (x-5):<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%28a%28x-5%29%5En%29%2F%28%28x%2B3%29%28x-3%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%28a%28x-5%29%5En%29%2F%28%28x%2B3%29%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Horizontal asymptote at y=1 --> degrees of numerator and denominator are the same, and leading coefficients are the same.  So a=1; and the number of factors of (x-5) must be 2:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%28%28x-5%29%5E2%29%2F%28%28x%2B3%29%28x-3%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%28%28x-5%29%5E2%29%2F%28%28x%2B3%29%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "y-intercept 5/9....<br><BR>\n" );
document.write( "This is a problem; the given requirements are inconsistent.<br><BR>\n" );
document.write( "With the function we have at this point, the y-intercept is -25/9.<br><BR>\n" );
document.write( "If we add a constant factor to make the y-intercept 5/9, then we no longer have a horizontal asymptote at y=1.<br><BR>\n" );
document.write( "ANSWER: The given conditions are inconsistent; there is no rational function with all the given features.<br><BR>\n" );
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