document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=213460>Question 213460</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a question that I have been working on and I am wondering if I am on the right path.  The question is as follows:  Is the graph f(x) = x^1171 - 5^109 + 3 y-axis symmetric, origin symmetric, or neither one.  Explain your answer.\r<BR>\n" );
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document.write( "When working out the problem and replacing x with -x the reworked problem does not come out the same as the original so it is not y-axis symmetric.  Then when I multiple (-1) to both sides it does not come out to be the same as the original problem either.  So, I am saying that f(x)=x^11171 - 5^109 +3 is neither y-axis or origin symmetric.  Am I right with my analysis?\r<BR>\n" );
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document.write( "Lori </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #161280 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=161280\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+x%5E1171+-+5%5E109+%2B+3 ALIGN=MIDDLE  ALT=\"f%28x%29+=+x%5E1171+-+5%5E109+%2B+3\"   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%5E1171+-+5%5E109+%2B+3 ALIGN=MIDDLE  ALT=\"f%28-x%29+=+%28-x%29%5E1171+-+5%5E109+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E1171 ALIGN=MIDDLE  ALT=\"x%5E1171\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a positive number we'll call k.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-x%29%5E1171 ALIGN=MIDDLE  ALT=\"%28-x%29%5E1171\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a negative number we'll call -k.<BR>\n" );
document.write( "example:<BR>\n" );
document.write( "(2)^3 = 8<BR>\n" );
document.write( "(-2)^3 = -8<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+-+5%5E109+%2B+3 ALIGN=MIDDLE  ALT=\"k+-+5%5E109+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-k%29+-+5%5E109+%2B+3 ALIGN=MIDDLE  ALT=\"%28-k%29+-+5%5E109+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > so the equation is not symmetric about the y axis.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "is your equation symmetric about the origin?<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+f%28x%29+=+x%5E1171+-+5%5E109+%2B+3 ALIGN=MIDDLE  ALT=\"y+=+f%28x%29+=+x%5E1171+-+5%5E109+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "solve for -y and -y.<BR>\n" );
document.write( "equation becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y+=+%28-x%29%5E1171+-+5%5E109+%2B+3 ALIGN=MIDDLE  ALT=\"-y+=+%28-x%29%5E1171+-+5%5E109+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "before we were able to show that if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E1171+=+k ALIGN=MIDDLE  ALT=\"x%5E1171+=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-x%29%5E1171+=+-k ALIGN=MIDDLE  ALT=\"%28-x%29%5E1171+=+-k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we use that again to get our equations to become:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+k+-+5%5E109+%2B+3 ALIGN=MIDDLE  ALT=\"y+=+k+-+5%5E109+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y+=+-k+-+5%5E109+%2B+3 ALIGN=MIDDLE  ALT=\"-y+=+-k+-+5%5E109+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "multiply the second equation by -1 to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+k+%2B+5%5E109+-+3 ALIGN=MIDDLE  ALT=\"y+=+k+%2B+5%5E109+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this is not the same as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+k+-+5%5E109+%2B+3 ALIGN=MIDDLE  ALT=\"y+=+k+-+5%5E109+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the equations are not symmetric about the origin either.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "an example of an equation that is symmetric about the origin would be:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%282x%5E2+%2B+5%29%2F7x ALIGN=MIDDLE  ALT=\"y+=+%282x%5E2+%2B+5%29%2F7x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "replace y with -y and replace x with -x to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y+=+%282%2A%28-x%29%5E2+%2B+5%29%2F7%28-x%29 ALIGN=MIDDLE  ALT=\"-y+=+%282%2A%28-x%29%5E2+%2B+5%29%2F7%28-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y+=+%282x%5E2+%2B+5%29%2F-7x ALIGN=MIDDLE  ALT=\"-y+=+%282x%5E2+%2B+5%29%2F-7x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply both sides of this equation by (-1) to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-%282x%5E2+%2B+5%29+%2F+-7x ALIGN=MIDDLE  ALT=\"y+=+-%282x%5E2+%2B+5%29+%2F+-7x\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%282x%5E2+%2B+5%29%2F7x ALIGN=MIDDLE  ALT=\"y+=+%282x%5E2+%2B+5%29%2F7x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the equations are identical when you replace y with -y and you replace x with -x.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%282x%5E2%2B5%29%2F7x ALIGN=MIDDLE  ALT=\"y+=+%282x%5E2%2B5%29%2F7x\"   DISABLED_style= \"max-width:90%; height:auto;\" > is symmetric about the origin<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "your equation of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E1171+-+5%5E109+%2B+3 ALIGN=MIDDLE  ALT=\"y+=+x%5E1171+-+5%5E109+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not.<BR>\n" );
document.write( "----- </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );