document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=712284>Question 712284</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am not sure if I am in the right place, but I need help my problem is:<BR>\n" );
document.write( "Test the equation for symmetry with respect to the x-axis, the y-axis, and the orgin<BR>\n" );
document.write( "x^2+xy^2+2y=1<BR>\n" );
document.write( "Is it:<BR>\n" );
document.write( "A. Symmetric with respect to the x-axis<BR>\n" );
document.write( "B. Symmetric with respect to the y-axis<BR>\n" );
document.write( "C. Symmetric with respect to the orgin<BR>\n" );
document.write( "D. Symmetric with respect to the x-axis, the y-axis, and the origin.\r<BR>\n" );
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document.write( "Thank you for any help you can give me. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #437851 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=437851\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If it was symmetrical with respect to the x-axis, then replacing each 'y' with '-y' should have no effect on the outcome\r<BR>\n" );
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document.write( "x^2+xy^2+2y=1\r<BR>\n" );
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document.write( "x^2+x(-y)^2+2(-y)=1\r<BR>\n" );
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document.write( "x^2+xy^2-2y=1 ... notice the change\r<BR>\n" );
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document.write( "Since there's a change, the first and last equations are NOT the same. So x^2+xy^2+2y=1 is NOT symmetric with respect to the x-axis\r<BR>\n" );
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document.write( "Similarly, if you replace each x with -x, you go from x^2+xy^2+2y=1 to x^2-xy^2+2y=1, which changes. So x^2+xy^2+2y=1 is NOT symmetric with respect to the y-axis \r<BR>\n" );
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document.write( "Because it's not symmetric with respect to either axis, it's NOT symmetric with respect to the origin\r<BR>\n" );
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document.write( "So it looks like none of the answer choices are correct. So there has to be something missing or there must be a typo somewhere. Please double check. Thanks. </SPAN>\n" );
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