document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1153467>Question 1153467</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an equation of a rational function that satisfies the following conditions:<BR>\n" );
document.write( "• Vertical asymptotes: x = −3<BR>\n" );
document.write( "• Horizontal asymptote: y=3/2<BR>\n" );
document.write( "• x -intercept: 5<BR>\n" );
document.write( "• Hole at x =2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #775689 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</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=775689\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "vertical asymptote at x = -3:<BR>\n" );
document.write( "This requires a factor of (x+3) in the denominator, without a like factor in the numerator:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28x%2B3%29 ALIGN=MIDDLE  ALT=\"1%2F%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "horizontal asymptote at y = 3/2:<BR>\n" );
document.write( "(We will take care of this last)<br><BR>\n" );
document.write( "x-intercept at x=5:<BR>\n" );
document.write( "This requires a factor of (x-5) in the numerator, without a like factor in the denominator:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%2F%28x%2B3%29 ALIGN=MIDDLE  ALT=\"%28x-5%29%2F%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Hole at x=2:<BR>\n" );
document.write( "This requires factors of (x-2) in BOTH numerator and denominator:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-5%29%28x-2%29%29%2F%28%28x%2B3%29%28x-2%29%29 ALIGN=MIDDLE  ALT=\"%28%28x-5%29%28x-2%29%29%2F%28%28x%2B3%29%28x-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "horizontal asymptote at y = 3/2:<BR>\n" );
document.write( "This requires the numerator and denominator to be the same degree, with the ratio of leading coefficients 3:2.  The degrees of the numerator and denominator are the same at this point; we just need to add constant factors to make the ratio of the leading coefficients equal to 3/2.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%28x-5%29%28x-2%29%29%2F%282%28x%2B3%29%28x-2%29%29 ALIGN=MIDDLE  ALT=\"%283%28x-5%29%28x-2%29%29%2F%282%28x%2B3%29%28x-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "A graph showing the vertical asymptote at x = -3 and the x-intercept at x=5:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C%283%28x-5%29%28x-2%29%29%2F%282%28x%2B3%29%28x-2%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "A graph showing the horizontal asymptote at y = 3/2:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-100%2C100%2C-10%2C10%2C%283%28x-5%29%28x-2%29%29%2F%282%28x%2B3%29%28x-2%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The graphing utility used on this site won't show the hole in the graph at x=2.  A good graphing calculator like the TI-83 will show it if you graph the function on a very small range of values of x either side of x=2.<br> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );