document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=43101>Question 43101</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help with this:\r<BR>\n" );
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document.write( "Is the following symmetric with respect to the x axis, y axis, origin, or no symmetry?\r<BR>\n" );
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document.write( "y= (1)/(x^2 + 1)\r<BR>\n" );
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document.write( "to clear up my writing, x^2 is the same as x squared.\r<BR>\n" );
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document.write( "thanks \r<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 #28137 by </B><A HREF=/tutors/aboutme.mpl?userid=ilana><B>ilana(307)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ilana><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=28137\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can just test values.  If it is symmetric wrt (with respect to) the x-axis, then a value of y will give you the same x as -y.  If it is symmetric wrt the y-axis, a value for x will give you the same y as -x.  And if it is symmetric wrt the origin, then (x,y) will become (-x,-y).<BR>\n" );
document.write( "So, let's test each.  If we plug in any x and any -x, the corresponmding y will be the same because x only appears once in this equation, and it is x^2.  So this is symmetric wrt the y-axis.  If we try to do the same for y, we see that a negative value for y will have no corresponding x (since 1/(x^2 + 1) is always positive).  So this is not symmetric wrt the x-axis.  And finally, since it never goes below the x-axis, it cannot be symmetric wrt the origin.  So it symmetric only wrt the y-axis. </SPAN>\n" );
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