document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1127528>Question 1127528</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine algebraically whether the function f(x)=x^3-2x+1 is odd, even, 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 #743934 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=743934\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To do this, you take the function and plug <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x ALIGN=MIDDLE  ALT=\"-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=simplify ALIGN=MIDDLE  ALT=\"simplify\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "If you end up with the exact same function that you started with (that is, if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f+%28-x%29+=+f+%28x%29 ALIGN=MIDDLE  ALT=\"f+%28-x%29+=+f+%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so all of the signs are the same), then the function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=even ALIGN=MIDDLE  ALT=\"even\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "If you end up with the exact opposite of what you started with (that is, if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f+%28-x%29+=+-f+%28x%29 ALIGN=MIDDLE  ALT=\"f+%28-x%29+=+-f+%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so all of the signs are switched), then the function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=odd ALIGN=MIDDLE  ALT=\"odd\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "In all other cases, the function is \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=neither ALIGN=MIDDLE  ALT=\"neither\"   DISABLED_style= \"max-width:90%; height:auto;\" > even nor odd\".\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+x%5E3+-+2+x+%2B+1+ ALIGN=MIDDLE  ALT=\"f%28x%29+=+x%5E3+-+2+x+%2B+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-x%29+=+%28-x%29%5E3+-+2+%28-x%29+%2B+1+ ALIGN=MIDDLE  ALT=\"f%28-x%29+=+%28-x%29%5E3+-+2+%28-x%29+%2B+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-x%29+=+-x%5E3+%2B+2+x+%2B+1 ALIGN=MIDDLE  ALT=\"f%28-x%29+=+-x%5E3+%2B+2+x+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f+%28-x%29+%3C%3E+f+%28x%29 ALIGN=MIDDLE  ALT=\"f+%28-x%29+%3C%3E+f+%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > =>is not an <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=even ALIGN=MIDDLE  ALT=\"even\"   DISABLED_style= \"max-width:90%; height:auto;\" > function\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "check if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f+%28-x%29+=+-f+%28x%29 ALIGN=MIDDLE  ALT=\"f+%28-x%29+=+-f+%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-x%29+=+-%28x%5E3+-2+x+%2B+1%29+%0D%0A%7B%7B%7Bf%28-x%29+=+-x%5E3+%2B2+x+-+1+ ALIGN=MIDDLE  ALT=\"f%28-x%29+=+-%28x%5E3+-2+x+%2B+1%29+%0D%0A%7B%7B%7Bf%28-x%29+=+-x%5E3+%2B2+x+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f+%28-x%29%3C%3E+-f+%28x%29 ALIGN=MIDDLE  ALT=\"f+%28-x%29%3C%3E+-f+%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > =>is not an <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=odd+ ALIGN=MIDDLE  ALT=\"odd+\"   DISABLED_style= \"max-width:90%; height:auto;\" > function\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "so, answer is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=neither ALIGN=MIDDLE  ALT=\"neither\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );