An ordered pair consists of the following things written in that order
1. A left parentheses "("
2. A number, called the first coordinate, or x-coordinate
3. A comma
4. A number, called the second coordinate, or y-coordinate
5. A right parentheses ")"
Here are some examples of ordered pairs:
(7,4), (8,8) (5,1), (7,0), (0,0) etc.
Every ordered pair starts with a "(" on the left end, then a number,
then a comma, then another number, and finally a ")" on the right end.
A function is a set of ordered pairs, enclosed between braces { } such that no
two have the same first coordinate or x-coordinate. It doesn't matter if two
have the same second coordinate or y-coordinate. It would still be a function
as long as no two first coordinates are the same.
Here is a set of ordered pairs which model a function:
{ (7,2), (1,1), (8,1), (4,2), (3,11) }
It models a function because all of the red numbers (first coordinates) are DIFFERENT. It doesn't matter that some of the blue numbers (second coordinates)
are THE SAME. It would still models a function whether any of the blue numbers
were the same or not.
All we have to do to change that set of ordered pairs so that it DOES NOT
model a function is to change one or more of the red numbers so that two will
have the same first coordinates, (red number). Like this:
{ (7,2), (1,1), (8,1), (4,2), (1,11) }
I changed the last ordered pair (3,11) to (1,11). That keeps the
set of five ordered pairs from modeling a function because it now has
two ordered pairs with the same first coordinate 1.
You can made them up by the hundreds. Just put two or more ordered pairs
in it that have the same first coordinate, so that it will NOT model a function.
You can tell why it doesn't model a function by telling which first coordinates
are the same.
Edwin
