Question 353865
Any set of ordered pairs of numbers is called "a relation".

Here is an example of a relation which is not a function:

{(<font color = "red">1</font>,<font color = "blue">-5</font>), (<font color = "red">3</font>,<font color = "blue">4</font>), (<font color = "red">-7</font>,<font color = "blue">5</font>), (<font color = "red">3</font>,<font color = "blue">9</font>), (<font color = "red">2</font>}

Its domain is the set of all first coordinates 

{<font color = "red">-7</font>,<font color = "red">1</font>,<font color = "red">2</font>,<font color = "red">3</font>,<font color = "red">5</font>}

Its range is the set of all second coordinates:

{<font color = "blue">-5</font>,<font color = "blue">4</font>,<font color = "blue">5</font>,<font color = "blue">9</font>}

However this relation is not labeled "a function" because 
the two ordered pairs (<font color = "red">3</font>,<font color = "blue">4</font>) and (<font color = "red">3</font>,<font color = "blue">9</font>) have the same first
coordinate <font color = "red">3</font>.  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.

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Here is an example of a relation which is also a function:

{(<font color = "red">3</font>,<font color = "blue">7</font>), (<font color = "red">-3</font>,<font color = "blue">0</font>), (<font color = "red">-6</font>,<font color = "blue">-8</font>), (<font color = "red">8</font>,<font color = "blue">7</font>), (<font color = "red">723</font>,<font color = "blue">-8</font>)}

Its domain is the set of all first coordinates 

{<font color = "red">-6</font>,<font color = "red">-3</font>,<font color = "red">3</font>,<font color = "red">8</font>,<font color = "red">723</font>}

Its range is the set of all second coordinates:

{<font color = "blue">-8</font>,<font color = "blue">0</font>,<font color = "blue">7</font>}

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 (<font color = "red">3</font>,<font color = "blue">7</font>) and (<font color = "red">8</font>,<font color = "blue">7</font>) have the same second coordinate
coordinate <font color = "blue">7</font>. It also does not matter
that the two ordered pairs (<font color = "red">-6</font>,<font color = "blue">-8</font>) and (<font color = "red">723</font>,<font color = "blue">-8</font>) have the same second coordinate
coordinate <font color = "blue">-8</font>.  
 
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</pre>