document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=269853>Question 269853</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi. I am having trouble with the following problem. I understand everything except for the x-intercept part. I would greatly appreciate your help,<BR>\n" );
document.write( "Thanks in advance.\r<BR>\n" );
document.write( "\n" );
document.write( "Find an equation of a rational function f  that satisfies the conditions:<BR>\n" );
document.write( "vertical asymptotes: x = - 2, x = 0<BR>\n" );
document.write( "horizontal asymptote: y = 0<BR>\n" );
document.write( "x-intercept: 5; f (6) = 1  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #197693 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=197693\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find an equation of a rational function f that satisfies the conditions:<BR>\n" );
document.write( "vertical asymptotes: x = - 2, x = 0<BR>\n" );
document.write( "we can write a general form as<BR>\n" );
document.write( "(i) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28ax%2Bb%29%2F%28x%28x%2B2%29%29%29 ALIGN=MIDDLE  ALT=\"y+=+%28ax%2Bb%29%2F%28x%28x%2B2%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "horizontal asymptote: y = 0<BR>\n" );
document.write( "This means as x approaches infinity, then the function approaches zero. This happens when the degree of the numerator is less  than the degree of the denominator<BR>\n" );
document.write( "we keep our function at<BR>\n" );
document.write( "(ii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28ax%2Bb%29%2F%28x%28x%2B2%29%29%29 ALIGN=MIDDLE  ALT=\"y+=+%28ax%2Bb%29%2F%28x%28x%2B2%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "x-intercept: 5<BR>\n" );
document.write( "If y = 0 , then x = 5.<BR>\n" );
document.write( "From (ii) we get<BR>\n" );
document.write( "(iii)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285a%2Bb%29%2F%285%285%2B2%29%29+=+0 ALIGN=MIDDLE  ALT=\"%285a%2Bb%29%2F%285%285%2B2%29%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "cross multiply to get<BR>\n" );
document.write( "5a+b = 0<BR>\n" );
document.write( "solving for a , we get<BR>\n" );
document.write( "(iv) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+-b%2F5 ALIGN=MIDDLE  ALT=\"a+=+-b%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "f (6) = 1<BR>\n" );
document.write( "means that if x = 6, then y = 1.<BR>\n" );
document.write( "From (i) and (iv) we get<BR>\n" );
document.write( "(vi) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+=+%286%28-b%2F5%29%2Bb%29%2F%286%286%2B2%29%29%29 ALIGN=MIDDLE  ALT=\"1+=+%286%28-b%2F5%29%2Bb%29%2F%286%286%2B2%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "cross multiplying we get<BR>\n" );
document.write( "(vii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48+=+-6b%2F5+%2B+b ALIGN=MIDDLE  ALT=\"48+=+-6b%2F5+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply by common denominator of 5, we get<BR>\n" );
document.write( "(viii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240+=+-6b+%2B+5b ALIGN=MIDDLE  ALT=\"240+=+-6b+%2B+5b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "solving for b, we get<BR>\n" );
document.write( "(ix) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+-240 ALIGN=MIDDLE  ALT=\"b+=+-240\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "This means that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+48 ALIGN=MIDDLE  ALT=\"a+=+48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and our equation is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%2848x-240%29%2F%28x%28x%2B2%29%29%29 ALIGN=MIDDLE  ALT=\"y+=+%2848x-240%29%2F%28x%28x%2B2%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );