Question 470900: Is the following relation a function? (1, 2), (3, 4), (5, 5)?
Found 2 solutions by nerdybill, MathLover1:
Answer by nerdybill(7384)   (Show Source):
Answer by MathLover1(20849)  (Show Source):
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Is the following relation a function? (1, 2), (3, 4), (5, 5)
recall: A  is  a  of   .
There is absolutely nothing special at all about the numbers that are in a relation. In other words,   of numbers  a so long as these numbers come in pairs.
The  and  of a relation:
The is the set of all the first numbers of the ordered pairs . In other words, the domain is all of the  .
The is the set of the second numbers in each pair, or the  .
In the relation above the is { 1, 3, 5 }
And the is { 2, 4, 5 }
 } makes a a  ?
 are a  kind of relation .
At first glance, a function looks just like a relation. It's a set of ordered pairs such as { (1, 2), (3, 4), (5, 5)}
Like a relation, a has a domain and range made up of the  and  values of ordered pairs.
In mathematics, what distinguishes a function from a relation is that   value in a function has  and    .
Since relation (1, 2), (3, 4), (5, 5) has   value for  value, this relation  a .
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