# Graphs and Graphing - Representing Ordered Pairs, Bar Graphs, Scatter Graphs, Line Graphs, Practical Applications

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set relation representation function

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.

## Additional Topics

In 1637, René Descartes (1594-1650), the French mathematician and philosopher, published a book entitled Géométrie, in which he applied algebraic methods to the study of geometry. In the book, Descartes described a system (now called the rectangular coordinate system or the Cartesian coordinate system) for using points in a plane to represent ordered pairs. Given any two sets …

A bar graph is used to picture the relationship between a relatively small number of objects, such as information listed in tabular form. Tables often represent mathematical relations, in that they consist of ordered pairs (listed in rows) for which the first and second elements of each pair (listed in separate columns) are related in a specific way. For example, a department store receipt is a re…

The scatter graph is similar to the bar graph in that it is used to represent relations containing a small number of ordered pairs. However, it differs from the bar graph in that both axes can be used to represent sets of real numbers. Since it is not feasible to represent pairs of real numbers with bars that have some width, ordered pairs of the relation are plotted by marking the corresponding p…

Very often, a function is defined by an equation relating elements from the set of real numbers to other elements, also from the set of real numbers. When this is the case the function will usually contain an infinite number of ordered pairs. For instance, if both X and Y correspond to the set of real numbers, then the equation y = 2x + 3 defines a function, specifically the set of ordered pairs (…

There are many practical applications of graphs and graphing. In the sciences and engineering, sets of numbers represent physical quantities. Graphing the relationship between these quantities is an useful tool for understanding nature. One specific example is the graphing of current versus voltage, used by electrical engineers, to picture the behavior of various circuit components. The rectangula…

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