document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=142821>Question 142821</A>: <I><SPAN STYLE=\"word-break: break-all;\"> which of these sets represents a function?..\r<BR>\n" );
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document.write( "(2,-2,), (3, -2), (2,3)        or\r<BR>\n" );
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document.write( "(9,pie), (5,7), (4,pie)        or\r<BR>\n" );
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document.write( "both    or    neither\r<BR>\n" );
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document.write( "PS: When I say pie I mean the 3.14 sign thing... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #103914 by </B><A HREF=/tutors/aboutme.mpl?userid=nabla><B>nabla(475)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nabla><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=103914\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Functions must pass the vertical line test, which is to say that they must not be multi-valued per x. Thus, having points sharing x coordinates with different y coordinates is a no-no.\r<BR>\n" );
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document.write( "Your answer is, from the reasoning I have supplied, the first choice (2,-2,), (3, -2), (2,3) because x=2 is multi-valued. For a counter-example, consider the simple graph of f(x)=x^2. This is obviously a function. But, as you can see by the graph, different x values take on the same y values (namely, their opposites):<BR>\n" );
document.write( "(-2)^2=2^2=4\r<BR>\n" );
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document.write( "By the way, pi is probably the most important mathematical constant there is. It represents the ratio of a circle's circumference to its diameter. That is, how long it is around over how wide it is. For future mathematical applications it's probably best to memorize it to, say, 5 decimal places. pi=3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510... </SPAN>\n" );
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