Graphs and Graphing

In mathematics, a graph is a geometric representation, a picture, of a relation or function. A relation is a subset of the set of all ordered pairs (x,y) for which each x is a member of some set X and each y is a member of another set Y. A specific relationship between each x and y determines which ordered pairs are in the subset. A function is a similar set of ordered pairs, with the added restriction that no two ordered pairs have the same first member. A graph, then, is a pictorial representation of the ordered pairs that comprise a relation or function. At the same time, it is a pictorial representation of the relationship between the first and second elements of each of the ordered pairs.