document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1031765>Question 1031765</A>: <I><SPAN STYLE=\"word-break: break-all;\"> f(x)=2x^2-1<BR>\n" );
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document.write( "a f(5)<BR>\n" );
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document.write( "c f(-x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #646427 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=646427\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%282x%5E2-1%29%2F%28x%5E2%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%282x%5E2-1%29%2F%28x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%285%29+=+%282%285%29%5E2-1%29%2F%28%285%29%5E2%29 ALIGN=MIDDLE  ALT=\"f%285%29+=+%282%285%29%5E2-1%29%2F%28%285%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace EVERY copy of x with 5\r<BR>\n" );
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document.write( "(b)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%282x%5E2-1%29%2F%28x%5E2%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%282x%5E2-1%29%2F%28x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-5%29+=+%282%28-5%29%5E2-1%29%2F%28%28-5%29%5E2%29 ALIGN=MIDDLE  ALT=\"f%28-5%29+=+%282%28-5%29%5E2-1%29%2F%28%28-5%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace EVERY copy of x with -5\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-5%29+=+%282%2825%29-1%29%2F%2825%29 ALIGN=MIDDLE  ALT=\"f%28-5%29+=+%282%2825%29-1%29%2F%2825%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > See note below\r<BR>\n" );
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document.write( "Note: squaring something like -5 yields a positive result since (-5)^2 = (-5)*(-5) = +25\r<BR>\n" );
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document.write( "(c)\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+=+%282%28-x%29%5E2-1%29%2F%28%28-x%29%5E2%29 ALIGN=MIDDLE  ALT=\"f%28-x%29+=+%282%28-x%29%5E2-1%29%2F%28%28-x%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace EVERY copy of x with -x\r<BR>\n" );
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document.write( "Now because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-x%29%5E2+=+x%5E2 ALIGN=MIDDLE  ALT=\"%28-x%29%5E2+=+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (based on the note above) this means that we end up with \r<BR>\n" );
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document.write( "which is the same as the original function. Only the left side is different. Because <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;\" >, for all values of x in the domain of f(x), this means that f(x) is an even function. It is symmetric with respect to the y axis. </SPAN>\n" );
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