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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 ?
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1 Answer

In answering each of these questions remember how a function is defined in term the of input and output. 
 
A function is a relationship in which each input has only one output. To check for a function look at the input and its output.
Is there another piece of data that has the same input but a different output? If there is, then it is not a function
 
Example: a table of values from the function f(x) = +/- √x
 
                                        x           f(x)
 
                                        0             0
                                        1             -1
                                        1             1
                                        4             -2
                                        4             2
                                        9             -3
                                        9             3
 
This is not a function because for the input 1, I can have output 1 or output -1.
 
Use that test for each of the 3 questions and you should be able to answer them correctly.