document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=546688>Question 546688</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the rational function: f(x)=7x / x^2-16<BR>\n" );
document.write( "Find<BR>\n" );
document.write( "a. The domain\r<BR>\n" );
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document.write( "b. All intercepts\r<BR>\n" );
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document.write( "c. All asymptotes </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #359288 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=359288\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given the rational function: f(x)=7x / x^2-16<BR>\n" );
document.write( "Find<BR>\n" );
document.write( "a. The domain <BR>\n" );
document.write( "When checking domain look for terms with sqrt and zeros in the denominator which would make function undefined. Since there are no sqrts in given equation, check for zeros in the denominator.<BR>\n" );
document.write( "x^2-16=0<BR>\n" );
document.write( "(x+4)(x-4)=0<BR>\n" );
document.write( "x=-4 and x=4<BR>\n" );
document.write( "domain:{x|x&#8800;-4, x&#8800;4}, or (-&#8734;,-4) U (-4, 4) U (4, &#8734;)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "b. All intercepts<BR>\n" );
document.write( "x-intercepts, set y=0, then solve for x<BR>\n" );
document.write( "7x / x^2-16=0<BR>\n" );
document.write( "7x=0<BR>\n" );
document.write( "x=0 (x-intercept)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "y-intercepts, set x=0, then solve for y<BR>\n" );
document.write( "f(0)=7x / x^2-16=0 (y-intercept)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "c. All asymptotes, set denominator=zero, then solve for x<BR>\n" );
document.write( "x^2-16=0<BR>\n" );
document.write( "(x+4)(x-4)=0<BR>\n" );
document.write( "x=-4 and x=4<BR>\n" );
document.write( "asymptotes are x=-4 and x=4 </SPAN>\n" );
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