document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200530>Question 1200530</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Explain how to use -x to determine if \r<BR>\n" );
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document.write( "a. f(x) is an even function.\r<BR>\n" );
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document.write( "b. f(x) is an odd function.\r<BR>\n" );
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document.write( "c. Use your explanation to show f(x)= x^3 - 8x is an even function, an odd function, or neither. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #834765 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=834765\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> here's a reference.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.mathsisfun.com/algebra/functions-odd-even.html\" target = \"_blank\">https://www.mathsisfun.com/algebra/functions-odd-even.html</a>\r<BR>\n" );
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document.write( "your example is f(x) = x^3 - 8x.\r<BR>\n" );
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document.write( "it will be even if f(x) = f(-x) for all values of x.<BR>\n" );
document.write( "you get:<BR>\n" );
document.write( "f(x) = x^3 - 8x<BR>\n" );
document.write( "f(-x) = (-x)^3 - 8(-x) = -x^3 + 8x<BR>\n" );
document.write( "since f(x) does not equal f(-x), then it is not an even function.\r<BR>\n" );
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document.write( "it will be odd if -f(x)= f(-x)<BR>\n" );
document.write( "-f(x) = -(x^3 - 8x) = -x^3 + 8x<BR>\n" );
document.write( "f(-x) = (-x)^3 - 8(-x) = -x^3 + 8x<BR>\n" );
document.write( "since -f(x) = f(-x), then it is an odd function.<BR>\n" );
document.write( "for example, let x = 2.<BR>\n" );
document.write( "-f(2) = -(2^3 - 8*2) = -(8-16) = -(-8) = 8<BR>\n" );
document.write( "f(-x) = (-2)^3 - 8*-2) = -8 -(-16) = -8 + 16 = 8.\r<BR>\n" );
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document.write( "check out the reference.<BR>\n" );
document.write( "it explains it pretty well.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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