document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=443325>Question 443325</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is a long question with multiple parts but is just one single question my professor gave me to work on but that I'm stuck on. <BR>\n" );
document.write( "Test: 1. y=x to the 4th minus 2x squared<BR>\n" );
document.write( "2. y=x to the 3rd minus 6x<BR>\n" );
document.write( "3. y=x squared + 2x + 1<BR>\n" );
document.write( "for symmetry with respect to:<BR>\n" );
document.write( "1. x-axis<BR>\n" );
document.write( "2. y-axis<BR>\n" );
document.write( "3. the origin (0,0)<BR>\n" );
document.write( "4. write them in function notation and say which one is even, odd, or neither?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #305794 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=305794\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. y=x to the 4th minus 2x squared<BR>\n" );
document.write( "2. y=x to the 3rd minus 6x<BR>\n" );
document.write( "3. y=x squared + 2x + 1<BR>\n" );
document.write( "for symmetry with respect to:<BR>\n" );
document.write( "1. x-axis<BR>\n" );
document.write( "2. y-axis<BR>\n" );
document.write( "3. the origin (0,0)<BR>\n" );
document.write( "4. write them in function notation and say which one is even, odd, or neither?<BR>\n" );
document.write( "--------------------------------------------------------------------------------I. y=x to the 4th minus 2x squared<BR>\n" );
document.write( "f(x) = x^4-2x^2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "1. Check f(x) = -f(x) <BR>\n" );
document.write( "x^4-2x^2 = -(x^4-2x^2)<BR>\n" );
document.write( "Ans: no x-axis symmetry<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "2. Check f(x) = f(-x)<BR>\n" );
document.write( "x^4-2x^2 = (-x)^4-2(-x^2)<BR>\n" );
document.write( "x^4-2x^2 = x^4-2x^2<BR>\n" );
document.write( "Ans: yes so y-axis symmetry<BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "3rd: Check f(x) = -f(-x)<BR>\n" );
document.write( "x^4-2x^2 = -((-x)^4-2(-x)^2)<BR>\n" );
document.write( "x^4-2x2 = -(x^4-2x^2)<BR>\n" );
document.write( "Ans: no so no origin symmetry<BR>\n" );
document.write( "======================================<BR>\n" );
document.write( "Do the same for the other listed problems.<BR>\n" );
document.write( "Form f(x), -f(x), f(-x) and -f(-x)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "If f(x) = -f(-x) you have x-axis symmetry<BR>\n" );
document.write( "If f(x) = f(-x) you have y-axis symmetry<BR>\n" );
document.write( "If f(x) = -f(-x) you have origin symmetry<BR>\n" );
document.write( "=========================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );