document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=414471>Question 414471</A>: <I><SPAN STYLE=\"word-break: break-all;\"> is this function even odd or neither?<BR>\n" );
document.write( "f(x)= -7 lxl + 3x^2 + 5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #290704 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=290704\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, we need to find f(-x)\r<BR>\n" );
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document.write( "f(x)= -7 |x| + 3x^2 + 5\r<BR>\n" );
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document.write( "f(-x)= -7 |-x| + 3(-x)^2 + 5\r<BR>\n" );
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document.write( "f(-x)= -7|x| + 3x^2 + 5\r<BR>\n" );
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document.write( "Note: |-x| = |-1*x| = |-1|*|x| = 1*|x| = |x| since |xy| = |x|*|y|\r<BR>\n" );
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document.write( "So f(x) = f(-x). This means that the function is even.\r<BR>\n" );
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document.write( "Now let's find -f(x)\r<BR>\n" );
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document.write( "f(x)= -7 |x| + 3x^2 + 5\r<BR>\n" );
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document.write( "-f(x)= -(-7 |x| + 3x^2 + 5)\r<BR>\n" );
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document.write( "-f(x)= 7|x| - 3x^2 - 5\r<BR>\n" );
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document.write( "Since -f(x) does NOT equal f(-x), this means that the function is NOT odd.\r<BR>\n" );
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document.write( "So the function f(x) is only even.\r<BR>\n" );
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document.write( "If you need more help, email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com\">jim_thompson5910@hotmail.com</a>\r<BR>\n" );
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document.write( "Jim<BR>\n" );
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