document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=136391>Question 136391</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tutor Can you help me in determining whether the  function is even, odd or neither even or odd?\r<BR>\n" );
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document.write( "f(x)=x-|x| </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #99905 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=99905\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A function is even if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=f%28-x%29 ALIGN=MIDDLE  ALT=\"f%28x%29=f%28-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for all x in the domain of f.  A function is odd if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-f%28x%29=f%28-x%29 ALIGN=MIDDLE  ALT=\"-f%28x%29=f%28-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for all x in the domain of f.  If neither equation holds across the domain, the function is neither even nor odd.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-x%29=-x-abs%28-x%29=-x-abs%28x%29%3C%3Ex-abs%28x%29 ALIGN=MIDDLE  ALT=\"f%28-x%29=-x-abs%28-x%29=-x-abs%28x%29%3C%3Ex-abs%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Not even.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-f%28x%29=-%28x-abs%28x%29%29=-x%2Babs%28x%29%3C%3E-x-abs%28x%29=f%28-x%29 ALIGN=MIDDLE  ALT=\"-f%28x%29=-%28x-abs%28x%29%29=-x%2Babs%28x%29%3C%3E-x-abs%28x%29=f%28-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Not odd.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28%0D%0A600%2C600%2C-5%2C5%2C-5%2C5%2C%0D%0Agrid%281%29%2C%0D%0Agraph%28%0D%0A600%2C600%2C-5%2C5%2C-5%2C5%2C%0D%0Ax-abs%28x%29%2Cx-abs%28x%29%0D%0A%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note that the graph of the function is not symmetrical about the y-axis which it would be if it were even, nor is it symmetrical about the origin which it would be if it were odd. </SPAN>\n" );
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