Question 470900


Is the following relation a function? (1, 2), (3, 4), (5, 5)


recall: A {{{relation}}} is {{{just}}} a {{{set}}} of {{{ordered}}}{{{ pairs}}}. 

There is absolutely nothing special at all about the numbers that are in a relation. In other words, {{{any}}}{{{ bunch}}} of numbers {{{is}}} a {{{relation}}} so long as these numbers come in pairs.

The {{{domain}}} and {{{range}}} of a relation:

The {{{domain}}} is the set of all the first numbers of the ordered pairs . In other words, the domain is all of the {{{x-values}}}. 


The {{{range}}} is the set of the second numbers in each pair, or the {{{y-values}}}.
 
  
In the relation above the {{{domain}}} is { 1, 3, 5 } 

And the {{{range}}} is { 2, 4, 5 }


{{{What}}}} makes a {{{relation}}} a {{{function}}} ? 

{{{Functions}}}are a {{{special}}} 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 {{{function}}} has a domain and range made up of the {{{x }}}and {{{y}}} values of ordered pairs. 

In mathematics, what distinguishes a function from a relation is that {{{each}}}{{{ x}}} value in a function has {{{one}}} and {{{only}}}{{{ ONE}}} {{{y-value}}}.

Since relation (1, 2), (3, 4), (5, 5) has {{{ONLY}}}{{{ ONE}}}{{{ y}}} value for {{{each}}}{{{ x }}}value, this relation {{{IS}}} a {{{function}}}.