document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1113797>Question 1113797</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an equation of a rational function f that satisfies the given conditions.<BR>\n" );
document.write( "vertical asymptotes: x = &#8722;3, x = 0<BR>\n" );
document.write( "horizontal asymptote: y = 0<BR>\n" );
document.write( "x-intercept: 3; f(4) = 1 </SPAN>\n" );
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document.write( "(1) vertical asymptotes: x = &#8722;3, x = 0<br><BR>\n" );
document.write( "Vertical asymptotes (values of x where the function is undefined -- i.e., has no value) are caused by factors in the denominator that are equal to 0.  If there are asymptotes at x=-3 and x=0, then there are factors of (x+3) and x in the denominator.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2F%28%28x%2B3%29%28x%29%29 ALIGN=MIDDLE  ALT=\"a%2F%28%28x%2B3%29%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(2) horizontal asymptote: y = 0<br><BR>\n" );
document.write( "The horizontal asymptote is 0 if the degree of the numerator is less than the degree of the numerator.  We'll come back to this one....<br><BR>\n" );
document.write( "(3) x-intercept: 3<br><BR>\n" );
document.write( "An x-intercept (where the function value is 0) is caused by a factor in the numerator that is equal to 0.  If there is an x-intercept at x=3, there must be a factor of (x-3) in the numerator.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28x-3%29%2F%28%28x%2B3%29%28x%29%29 ALIGN=MIDDLE  ALT=\"a%28x-3%29%2F%28%28x%2B3%29%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Note that the degree of the numerator at this point is less than the degree of the denominator; so the condition for having a horizontal asymptote of y=0 is satisfied.  So we have all the factors of our rational function that contain variables; we now need to find the constant factor.<br><BR>\n" );
document.write( "(4) f(4) = 1<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%284-3%29%2F%28%284%2B3%29%284%29%29+=+1 ALIGN=MIDDLE  ALT=\"a%284-3%29%2F%28%284%2B3%29%284%29%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2F28+=+1 ALIGN=MIDDLE  ALT=\"a%2F28+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+28 ALIGN=MIDDLE  ALT=\"a+=+28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Our rational function is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28%28x-3%29%2F%28%28x%2B3%29%28x%29%29 ALIGN=MIDDLE  ALT=\"28%28x-3%29%2F%28%28x%2B3%29%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "A graph...<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C5%2C-50%2C150%2C28%28x-3%29%2F%28%28x%2B3%29%28x%29%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C5%2C-50%2C150%2C28%28x-3%29%2F%28%28x%2B3%29%28x%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );