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Answered

The tables below show the values of y corresponding to different values of x:






Table A




x

3 2 1


y

1 0 0




Table B




x

3 5 5


y

−2 1 2



Which statement is true for the tables?



Both Table A and Table B represent functions.


Both Table A and Table B do not represent functions.


Table A does not represent a function, but Table B represents a function.


Table A represents a function, but Table B does not represent a function.

Verified Answer :

freesparrow

Table A represent a function, and Table B does not.
Why?
Table to be a function, need to satisfy following conditions (look at the .jpeg image attached with this answer):
1. condition: In first circle, EVERY element has to be connected with SOME of the elements in second circle
2. condition: In first circle, there MUSTN'T be an element that has MORE THAN ONE connection with elements in second circle
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Table A satisfies BOTH of these conditions; that is why table A is indeed a function.
Table B satisfies FIRST condition but it does not satisfy the SECOND condition, that is why it is NOT a function.

View image freesparrow

Solution:

A function or mapping is defined as set of ordered pairs(x,y) such that for different x values there will be different y values or vice versa.for example , x= y +2 is a function,because for different y we will get different x and for no  two different , y values we get a unique x value. For two different y's we get two different x, then we can call it a function.

Table A    

            X               Y

            3                 1

             2                 0

             1                  0

As, each element of X is associated with unique element of Y, so this is a function.

Table B

X            Y

3           -2

5              1

5              2

Two same elements of X that is 5 has different images that is 1 as well as 2 . So this is not a function.

Option (4) →Table A represents a function, but Table B does not represent a function.

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