document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=730189>Question 730189</A>: <I><SPAN STYLE=\"word-break: break-all;\"> To determine if a function is odd even or neither.<BR>\n" );
document.write( "f(x) = x^3 - x^2. Ok substitute (-x)^3 - (-x)^2\r<BR>\n" );
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document.write( "-x^3 + x^2. How can I determine if it is odd even or neither. to me it is mixed the x^3 becomes, -x^3 and x^2 becomes -x^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #446539 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=446539\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It's neither because there's a mix of odd and even exponents.\r<BR>\n" );
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document.write( "If it was even, then you'd have all even exponents.\r<BR>\n" );
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document.write( "If it was odd, then you'd have all odd exponents.\r<BR>\n" );
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document.write( "This trick only works for polynomials.\r<BR>\n" );
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document.write( "-------------------------------------------------------------------\r<BR>\n" );
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document.write( "f(x) = x^3 - x^2\r<BR>\n" );
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document.write( "f(-x) = (-x)^3 - (-x)^2\r<BR>\n" );
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document.write( "f(-x) = -x^3 - x^2\r<BR>\n" );
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document.write( "So f(x) does NOT equal f(-x) which means that f(x) is NOT even.\r<BR>\n" );
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document.write( "f(x) = x^3 - x^2\r<BR>\n" );
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document.write( "-f(x) = -(x^3 - x^2)\r<BR>\n" );
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document.write( "-f(x) = -x^3 + x^2\r<BR>\n" );
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document.write( "-f(x) = -x^3 + x^2\r<BR>\n" );
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document.write( "So f(-x) does NOT equal -f(x) which means that f(x) is NOT odd.\r<BR>\n" );
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document.write( "Final answer: f(x) is neither even nor odd. </SPAN>\n" );
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