SOLUTION: How do you tell if a table or if a graph represents a function? 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

Question 21859: How do you tell if a table or if a graph represents a function?
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
X....A.....B......C......D......E
Y....P.....Q......Q......R......S.....T....U....V
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.
TWO QUESTIONS SHOULD BE ANSWERED WITH YES IF WE WERE TO CALL Y=F(X)...
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.
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.
THAT IS ALL IF THESE 2 QUESTIONS ARE ANSWERED IN YES THEN Y=F(X), does that help you understand better?

Found 2 solutions by venugopalramana, ushergurl:
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
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
X....A.....B......C......D......E
Y....P.....Q......Q......R......S.....T....U....V
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.
TWO QUESTIONS SHOULD BE ANSWERED WITH YES IF WE WERE TO CALL Y=F(X)...
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.
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.
THAT IS ALL IF THESE 2 QUESTIONS ARE ANSWERED IN YES THEN Y=F(X)
Answer by ushergurl(1) (Show Source): You can put this solution on YOUR website!
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
X....A.....B......C......D......E
Y....P.....Q......Q......R......S.....T....U....V
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.
TWO QUESTIONS SHOULD BE ANSWERED WITH YES IF WE WERE TO CALL Y=F(X)...
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.
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.
THAT IS ALL IF THESE 2 QUESTIONS ARE ANSWERED IN YES THEN Y=F(X).
Does that help you understands better?

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