Question 353865: Given the relations {(7,5), (-6,0), (2,3)}
{7,-6,2,-7}
this is how they are written exactly
domain is -6,2,7 range is 0,3,5 of the first one i am confused by the way the other one is written....
I need to find which is a function and I think it is the first set...am I right and why is the other one written like that
thank you so much
Answer by Edwin McCravy(20086)   (Show Source):
You can put this solution on YOUR website! Any set of ordered pairs of numbers is called "a relation".
Here is an example of a relation which is not a function:
{(1,-5), (3,4), (-7,5), (3,9), (2}
Its domain is the set of all first coordinates
{-7,1,2,3,5}
Its range is the set of all second coordinates:
{-5,4,5,9}
However this relation is not labeled "a function" because
the two ordered pairs (3,4) and (3,9) have the same first
coordinate 3. In ordered to be labeled "a function", a relation
cannot contain two ordered pairs with the same first coordinate.
It does not matter about second coordinates being the same,
just the first coordinates can't be the same.
---------------------------------------------------------
Here is an example of a relation which is also a function:
{(3,7), (-3,0), (-6,-8), (8,7), (723,-8)}
Its domain is the set of all first coordinates
{-6,-3,3,8,723}
Its range is the set of all second coordinates:
{-8,0,7}
This relation IS labeled "a function" because none of the ordered
pairs it contains have the same first coordinate. It does not matter
that the two ordered pairs (3,7) and (8,7) have the same second coordinate
coordinate 7. It also does not matter
that the two ordered pairs (-6,-8) and (723,-8) have the same second coordinate
coordinate -8.
So in short to find out if a relation is a function, you just look at
the first coordinates and if none of them are the same, then you know
it is a function, but if two first coordinates are the same, then the
relation is not a function.
Now, there is a special kind of function, called a "one-to-one function",
which you will study later, that also has no two second coordinates the
same. However, for now, just to be a function, there may be two or more
second coordinates the same, but just no two first coordinates the same.
Edwin
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