A function is a set of ordered pairs that has no two ordered
pairs with the same FIRST or x-coodinates.
A set of ordered pairs is a function if and only if no
x-coordinate is used more than once.
{(1,4),(8,5),(3,8),(7,0)} is a function because none of the
first coordinates (x-coordinates) are the same.
{(1,4),(8,4),(3,4),(7,0)} is a function because none of the
first coordinates (x-coordinates) are the same, even though
three of them have the same second coordinates. It doesn't
matter about the 2nd coordinates (the 2nd or y-coordinates).
They can be repeated, but the 1st or x-coordinates cannot be
repeated.
{(4,7),(8,4),(4,3),(7,0)} is NOT a function because 4 appears
as an x-coordinate in both (4,7) and (4,3). A first coordinate
cannot be repeated like that, but a second coordinate can be
repeated. If any two first coordinates (x-coordinates) are
the same in two different ordered pairs, the set of ordered
pairs is not a function.
Edwin
