document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198361>Question 1198361</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which of the following is  a function?\r<BR>\n" );
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document.write( "A) [(1,2),(3,2),(1,3)]<BR>\n" );
document.write( "B) [(1,3),(2,3),(6,7)]<BR>\n" );
document.write( "C) [(9,4),(2,1),(9,6)]<BR>\n" );
document.write( "D) [(6,2),(8,3),(6,4)]<BR>\n" );
document.write( "E) [(2,6),(2,7),(2,9)]\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #831937 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=831937\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Choice A is not a function because the input x = 1 has multiple outputs (y = 2 and y = 3 at the same time). <BR>\n" );
document.write( "A function is only possible if any given x input leads to exactly one y output.\r<BR>\n" );
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document.write( "Choices C, D, and E are also not functions for this similar reasoning.\r<BR>\n" );
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document.write( "Choice B on the other hand is a function.<BR>\n" );
document.write( "None of the x coordinates repeat themselves. Each item is listed exactly once. <BR>\n" );
document.write( "The y values can repeat, but the function wouldn't be one-to-one.\r<BR>\n" );
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document.write( "A visual alternative tool is to use the vertical line test. <BR>\n" );
document.write( "If it is possible to draw a vertical line through more than one point, then that relation is not a function. <BR>\n" );
document.write( "In such a case, it is said this relation fails the vertical line test.<BR>\n" );
document.write( "This is what it looks like for the points from choice A<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C500%2C-5%2C5%2C-5%2C5%2C%0D%0Agraph%28500%2C500%2C-5%2C5%2C-5%2C5%2C-100%29%2C%0D%0Ablue%28circle%281%2C2%2C0.05%29%29%2C%0D%0Ablue%28circle%281%2C2%2C0.07%29%29%2C%0D%0Ablue%28circle%281%2C2%2C0.1%29%29%2C%0D%0Ablue%28circle%283%2C2%2C0.05%29%29%2C%0D%0Ablue%28circle%283%2C2%2C0.07%29%29%2C%0D%0Ablue%28circle%283%2C2%2C0.1%29%29%2C%0D%0Ablue%28circle%281%2C3%2C0.05%29%29%2C%0D%0Ablue%28circle%281%2C3%2C0.07%29%29%2C%0D%0Ablue%28circle%281%2C3%2C0.1%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The points (1,2) and (1,3) make this relation fail the vertical line test. I'll let you form the graphs of the other answer choices.\r<BR>\n" );
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document.write( "Answer: <font color=red>Choice B</font><BR>\n" );
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