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Linear Function.............................

The following table contains the names of the nine America Leaque All stars from 2008,along with the players AL team.

Name: Team
Cliff Lee(P) Cleveland Indians
Joe Mauer(C) Minnesota Twins
Kevin Youkilis(1B) Boston Red Sox
Dustin Pedroia(2B) Boston Red Sox
Derek Jeter(SS) New York Yankees
Alex Rodriques(3B) New York Yankees
Manny Ramirez(LF) Boston Red Sox
Josh Hamiltion(CF) Texas Rangers
Ichiro Suzuki(RF) Seattle Mariners

(1) Would a relation that took a player's name as an input and listed his AL team as an output be a function? why or why not.

(2) Could a function be defined in the opposite direction,with the name of the AL team as the input and the All-star player's name as the output? why or why not?

(3) Could a function be defined with a woman as an input and her child as an output?why or why not ?

1 Answer by Expert Tutors

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Beth L. | Patient, Knowledgeable and Very Qualified Mathematics TutorPatient, Knowledgeable and Very Qualifie...
1)  No, not a function.  In order to be a function, there would need to be some math corrolation between the person's name and the team (the person could be on any team, it just so happens they are on the teams listed, in other words, they could CHANGE teams (and many players do during baseball season through trades, etc).  This would be a "dot graph" with several players being on the same team (3 for Boston Red Sox, 2 from Yankees).  
2)  This would be like a bar graph with the team listed (such as Boston being on the X axis), and having several Y's (players) on that team.  So this would not be a function either.
3)  This one is tricky but I believe so if you are talking about gene traits, genetics (color of hair, eyes, disease traits, etc).  In genetics depending on who in the family has the trait (since half of the chromosomes come from the father and half from the mother), and the father and mother got their traits from the grandparents, there is a probability of a child having a certain color of eyes or hair.  Since PROBABILITY has a math formula, then Yes, this could be a function.


1) Hmmm, there is a correlation provided. It is the table. Since each input is unique, providing a single output, that could qualify as a function.
2) Since the inputs are not unique (there are several entries with the same team), you could not provide a single output, so that would probably not qualify as a function.
3) Likely yes.