document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=671829>Question 671829</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For the given equation, list the intercepts and test for symmetry.\r<BR>\n" );
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document.write( "y= 3x/x^2 +81<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #417653 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=417653\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Substitute 0 for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\">:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ \frac{3(0)}{(0)^2\ +\ 81}\ =\ \frac{0}{81}\ =\ 0\">\r<BR>\n" );
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document.write( "Hence both the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\"> intercepts are the origin, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(0,0\right)\">\r<BR>\n" );
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document.write( "A function is symmetric with respect to the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> axis iff <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(a)\ =\ -f(a)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{3x}{x^2\ +\ 81}\ \neq\ -\frac{3x}{x^2\ +\ 81}\">\r<BR>\n" );
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document.write( "Hence, <b>not</b> symmetrical with respect to the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> axis.\r<BR>\n" );
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document.write( "A function is symmetric with respect to the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\"> axis iff <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(a)\ =\ f(-a)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{3x}{x^2\ +\ 81}\ \neq\ \frac{3(-x)}{(-x)^2\ +\ 81}\ =\ -\frac{3x}{x^2\ +\ 81}\">\r<BR>\n" );
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document.write( "Hence, <b>not</b> symmetrical with respect to the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\"> axis.\r<BR>\n" );
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document.write( "A function is symmetric with respect to the origin iff <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(a)\ =\ -f(-a)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{3x}{x^2\ +\ 81}\ =\ -\frac{3(-x)}{(-x)^2\ +\ 81}\ =\ \frac{3x}{x^2\ +\ 81}\">\r<BR>\n" );
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document.write( "Hence, the function <b>is</b> symmetrical with respect to the origin.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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