document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=943443>Question 943443</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Show that the linear function f defined by<BR>\n" );
document.write( "f (x) = mx + b is an even function if and only if<BR>\n" );
document.write( "m = 0. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #575183 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=575183\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) is even when f(-x) = f(x) for all x in the domain.\r<BR>\n" );
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document.write( "f(x) = mx + b\r<BR>\n" );
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document.write( "f(-x) = m(-x) + b\r<BR>\n" );
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document.write( "f(-x) = -mx + b\r<BR>\n" );
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document.write( "Set f(-x) equal to f(x)\r<BR>\n" );
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document.write( "f(-x) = f(x)\r<BR>\n" );
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document.write( "-mx + b = mx + b\r<BR>\n" );
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document.write( "-mx + b<font color=\"red\">-b</font> = mx + b<font color=\"red\">-b</font> <font color=\"blue\"> ... Subtract b from both sides.</font>\r<BR>\n" );
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document.write( "-mx = mx\r<BR>\n" );
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document.write( "-mx<font color=\"red\">+mx</font> = mx<font color=\"red\">+mx</font><font color=\"blue\"> ... Add mx to both sides.</font>\r<BR>\n" );
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document.write( "0 = mx+mx\r<BR>\n" );
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document.write( "0 = 2mx\r<BR>\n" );
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document.write( "2mx = 0\r<BR>\n" );
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document.write( "2mx = 0 means m = 0 (since x is any number, it's not always 0, so m has to be zero) </SPAN>\n" );
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