document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=353865>Question 353865</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the relations {(7,5), (-6,0), (2,3)}  <BR>\n" );
document.write( "                    {7,-6,2,-7}   <BR>\n" );
document.write( "this is how they are written exactly\r<BR>\n" );
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document.write( "domain is -6,2,7  range is 0,3,5 of the first one    i am confused by the way the other one is written....<BR>\n" );
document.write( "I need to find which is a function and I think it is the first set...am I right and why is the other one written like that <BR>\n" );
document.write( "thank you so much </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #252957 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20086)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=252957\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Any set of ordered pairs of numbers is called \"a relation\".\r<BR>\n" );
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document.write( "Here is an example of a relation which is not a function:\r<BR>\n" );
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document.write( "{(<font color = \"red\">1</font>,<font color = \"blue\">-5</font>), (<font color = \"red\">3</font>,<font color = \"blue\">4</font>), (<font color = \"red\">-7</font>,<font color = \"blue\">5</font>), (<font color = \"red\">3</font>,<font color = \"blue\">9</font>), (<font color = \"red\">2</font>}\r<BR>\n" );
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document.write( "Its domain is the set of all first coordinates \r<BR>\n" );
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document.write( "{<font color = \"red\">-7</font>,<font color = \"red\">1</font>,<font color = \"red\">2</font>,<font color = \"red\">3</font>,<font color = \"red\">5</font>}\r<BR>\n" );
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document.write( "Its range is the set of all second coordinates:\r<BR>\n" );
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document.write( "{<font color = \"blue\">-5</font>,<font color = \"blue\">4</font>,<font color = \"blue\">5</font>,<font color = \"blue\">9</font>}\r<BR>\n" );
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document.write( "However this relation is not labeled \"a function\" because <BR>\n" );
document.write( "the two ordered pairs (<font color = \"red\">3</font>,<font color = \"blue\">4</font>) and (<font color = \"red\">3</font>,<font color = \"blue\">9</font>) have the same first<BR>\n" );
document.write( "coordinate <font color = \"red\">3</font>.  In ordered to be labeled \"a function\", a relation<BR>\n" );
document.write( "cannot contain two ordered pairs with the same first coordinate.<BR>\n" );
document.write( "It does not matter about second coordinates being the same,<BR>\n" );
document.write( "just the first coordinates can't be the same.\r<BR>\n" );
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document.write( "Here is an example of a relation which is also a function:\r<BR>\n" );
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document.write( "{(<font color = \"red\">3</font>,<font color = \"blue\">7</font>), (<font color = \"red\">-3</font>,<font color = \"blue\">0</font>), (<font color = \"red\">-6</font>,<font color = \"blue\">-8</font>), (<font color = \"red\">8</font>,<font color = \"blue\">7</font>), (<font color = \"red\">723</font>,<font color = \"blue\">-8</font>)}\r<BR>\n" );
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document.write( "Its domain is the set of all first coordinates \r<BR>\n" );
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document.write( "{<font color = \"red\">-6</font>,<font color = \"red\">-3</font>,<font color = \"red\">3</font>,<font color = \"red\">8</font>,<font color = \"red\">723</font>}\r<BR>\n" );
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document.write( "Its range is the set of all second coordinates:\r<BR>\n" );
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document.write( "{<font color = \"blue\">-8</font>,<font color = \"blue\">0</font>,<font color = \"blue\">7</font>}\r<BR>\n" );
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document.write( "This relation IS labeled \"a function\" because none of the ordered<BR>\n" );
document.write( "pairs it contains have the same first coordinate.  It does not matter<BR>\n" );
document.write( "that the two ordered pairs (<font color = \"red\">3</font>,<font color = \"blue\">7</font>) and (<font color = \"red\">8</font>,<font color = \"blue\">7</font>) have the same second coordinate<BR>\n" );
document.write( "coordinate <font color = \"blue\">7</font>. It also does not matter<BR>\n" );
document.write( "that the two ordered pairs (<font color = \"red\">-6</font>,<font color = \"blue\">-8</font>) and (<font color = \"red\">723</font>,<font color = \"blue\">-8</font>) have the same second coordinate<BR>\n" );
document.write( "coordinate <font color = \"blue\">-8</font>.  <BR>\n" );
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document.write( "So in short to find out if a relation is a function, you just look at<BR>\n" );
document.write( "the first coordinates and if none of them are the same, then you know<BR>\n" );
document.write( "it is a function, but if two first coordinates are the same, then the<BR>\n" );
document.write( "relation is not a function.\r<BR>\n" );
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document.write( "Now, there is a special kind of function, called a \"one-to-one function\",<BR>\n" );
document.write( "which you will study later, that also has no two second coordinates the <BR>\n" );
document.write( "same.  However, for now, just to be a function, there may be two or more<BR>\n" );
document.write( "second coordinates the same, but just no two first coordinates the same.\r<BR>\n" );
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document.write( "Edwin</pre>  </SPAN>\n" );
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