document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=21859>Question 21859</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you tell if a table or if a graph represents a function?<BR>\n" );
document.write( "Well, LET THE TABLE OR GRAPH SHOW X AND Y...WE SHALL SEE HOW OR WHEN WE SAY Y=F(X).LET THE VALUES OF X AND Y BE AS SHOWN BELOW<BR>\n" );
document.write( "X....A.....B......C......D......E<BR>\n" );
document.write( "Y....P.....Q......Q......R......S.....T....U....V<BR>\n" );
document.write( "SOME TIMES THEY ARE SHOWN AS ORDERED PAIRS (A,P),(B,Q),(C,Q),(D,R),(E,S).UNRELATED ELEMENTS LIKE T,U,V ARE LEFT ALONE.<BR>\n" );
document.write( "TWO QUESTIONS SHOULD BE ANSWERED WITH YES IF WE WERE TO CALL Y=F(X)...<BR>\n" );
document.write( "Q.1. IS EVERY ELEMENT OR VALUE UNDER X HAVE A CORRESPONDING ELEMENT OR VALUE UNDER Y..........WE FIND IT IS SO IN THIS CASE ...SO YES.NOTE THAT EVERY ELEMENT IN X SHOULD HAVE A CORRESPONDING ELEMENT(CALLED IMAGE) IN Y ,FOR Y=F(X),BUT NOT NECESSARILY THE OTHERWAY ROUND..WE FIND HERE THAT T,U,V IN Y ARE NOT ASSOCIATED WITH ANY ELEMENT IN X.THAT IS O.K.BUT SUPPOSE THERE IS ONE ELEMENT SAY F IN X WHICH IS NOT ASSOCIATED WITH ANY ELEMENT IN Y THEN IT IS NOT A FUNCTION.<BR>\n" );
document.write( "Q.2.ONE ELEMENT IN X CANNOT HAVE MORE THAN ONE IMAGE IN Y.WE FIND IT TO BE SO IN THIS CASE SO YES...NOTE AGAIN HERE 2 ELEMENTS IN A CAN HAVE SAME IMAGE IN Y AS IN THIS CASE BOTH B AND C HAVE SAME IMAGE Q...THAT IS O.K. BUT NOT THE OTHERWAY ROUND...THAT IS A CANNOT HAVE P AND ANOTHER SAY T AS ITS IMAGE..THAT IS IMAGE OF EVERY ELEMENT IN X SHALL BE UNIQUE.<BR>\n" );
document.write( "THAT IS ALL IF THESE 2 QUESTIONS ARE ANSWERED IN YES THEN Y=F(X), does that help you understand better?<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 #11434 by </B><A HREF=/tutors/aboutme.mpl?userid=ushergurl><B>ushergurl(1)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ushergurl><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=11434\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> WELL,LET THE TABLE OR GRAPH SHOW X AND Y...WE SHALL SEE HOW OR WHEN WE SAY Y=F(X).LET THE VALUES OF X AND Y BE AS SHOWN BELOW<BR>\n" );
document.write( "X....A.....B......C......D......E<BR>\n" );
document.write( "Y....P.....Q......Q......R......S.....T....U....V<BR>\n" );
document.write( "SOME TIMES THEY ARE SHOWN AS ORDERED PAIRS (A,P),(B,Q),(C,Q),(D,R),(E,S).UNRELATED ELEMENTS LIKE T,U,V ARE LEFT ALONE.<BR>\n" );
document.write( "TWO QUESTIONS SHOULD BE ANSWERED WITH YES IF WE WERE TO CALL Y=F(X)...<BR>\n" );
document.write( "Q.1. IS EVERY ELEMENT OR VALUE UNDER X HAVE A CORRESPONDING ELEMENT OR VALUE UNDER Y..........WE FIND IT IS SO IN THIS CASE ...SO YES.NOTE THAT EVERY ELEMENT IN X SHOULD HAVE A CORRESPONDING ELEMENT(CALLED IMAGE) IN Y ,FOR Y=F(X),BUT NOT NECESSARILY THE OTHERWAY ROUND..WE FIND HERE THAT T,U,V IN Y ARE NOT ASSOCIATED WITH ANY ELEMENT IN X.THAT IS O.K.BUT SUPPOSE THERE IS ONE ELEMENT SAY F IN X WHICH IS NOT ASSOCIATED WITH ANY ELEMENT IN Y THEN IT IS NOT A FUNCTION.<BR>\n" );
document.write( "Q.2.ONE ELEMENT IN X CANNOT HAVE MORE THAN ONE IMAGE IN Y.WE FIND IT TO BE SO IN THIS CASE SO YES...NOTE AGAIN HERE 2 ELEMENTS IN A CAN HAVE SAME IMAGE IN Y AS IN THIS CASE BOTH B AND C HAVE SAME IMAGE Q...THAT IS O.K. BUT NOT THE OTHERWAY ROUND...THAT IS A CANNOT HAVE P AND ANOTHER SAY T AS ITS IMAGE..THAT IS IMAGE OF EVERY ELEMENT IN X SHALL BE UNIQUE.<BR>\n" );
document.write( "THAT IS ALL IF THESE 2 QUESTIONS ARE ANSWERED IN YES THEN Y=F(X).<BR>\n" );
document.write( "Does that help you understands better? \r<BR>\n" );
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