document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=245882>Question 245882</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi i really need help with this question: Alex states that the relation below is not a function. Lillian says that it is a function. Who is correct? Explain your reasoning.\r<BR>\n" );
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document.write( "Relation { (13,14), (12,5) , (16,7), (13, 14), (-2, 33), (13, 14 }\r<BR>\n" );
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document.write( "Explanation:<BR>\n" );
document.write( "I'm not sure if it is a function or not, and i dont know how to explain it because of that.\r<BR>\n" );
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document.write( "Thanks -Drea  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #179546 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=179546\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "The given relation shows correspondence between input values (the left-hand numbers in the ordered pairs) and output values (the right-hand numbers).  A relation is a function if and only if there is only one output value for any given input value.  It is perfectly ok, and the relation is still a function, if two different input values give the same output value.  Just because your relation set has three identical elements, namely three instances of (13,14), you still only have one output for any given input.  Put in 13, you get 14.  This is most assuredly a function.\r<BR>\n" );
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document.write( "By contrast:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left{ (13,14),\, (12,5) ,\, (16,7),\, (13, 6),\, (-2, 33),\, (13, 14) \right}\"> \r<BR>\n" );
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document.write( "Would NOT be a function because an input of 13 would have an output of 14 or 6.\r<BR>\n" );
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document.write( "whereas:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left{ (13,14),\, (12,5) ,\, (16,5),\, (13, 14),\, (-2, 33),\, (13, 14) \right}\">\r<BR>\n" );
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document.write( "IS a function despite the fact that an input of 12 or 16 has an output of 5. \r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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