document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1146948>Question 1146948</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Give an example of a rational function h whose graph has the following properties.\r<BR>\n" );
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document.write( "vertical asymptote: x = -1 and x = 2<BR>\n" );
document.write( "horizontal asymptote: y = 3\r<BR>\n" );
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document.write( "x-intercept: (3, 0) </SPAN>\n" );
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document.write( "(1) vertical asymptote: x = -1 and x = 2<br><BR>\n" );
document.write( "This means there are factors of (x+1) and (x-2) in the denominator:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2F%28%28x%2B1%29%28x-2%29%29 ALIGN=MIDDLE  ALT=\"a%2F%28%28x%2B1%29%28x-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(2) x-intercept: (3, 0)<br><BR>\n" );
document.write( "This means there is a factor of (x-3) in the numerator:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%28x-3%29%29%2F%28%28x%2B1%29%28x-2%29%29 ALIGN=MIDDLE  ALT=\"%28a%28x-3%29%29%2F%28%28x%2B1%29%28x-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(3) horizontal asymptote: y = 3<br><BR>\n" );
document.write( "This means there is a constant factor of 3 in the numerator; and the degrees of the numerator and denominator are the same.  So, in addition to the constant factor 3, we need a second linear factor in the numerator.  It can be any linear factor; I chose x, meaning there is a second x-intercept at x=0:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%28x%29%28x-3%29%29%2F%28%28x%2B1%29%28x-2%29%29 ALIGN=MIDDLE  ALT=\"%283%28x%29%28x-3%29%29%2F%28%28x%2B1%29%28x-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Here is a graph:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C400%2C-10%2C10%2C-10%2C10%2C%283%28x%29%28x-3%29%29%2F%28%28x%2B1%29%28x-2%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "If the statement of the problem is supposed to imply that x=3 is the ONLY x-intercept, then we can make the second linear factor in the numerator (x-3) also.  Note that means the graph will be tangent to the x-axis at x=3:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%28x-3%29%5E2%29%2F%28x%2B1%29%28x-2%29%29 ALIGN=MIDDLE  ALT=\"%283%28x-3%29%5E2%29%2F%28x%2B1%29%28x-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Here is a graph:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C400%2C-10%2C10%2C-10%2C10%2C%283%28x-3%29%5E2%29%2F%28%28x%2B1%29%28x-2%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );