04Brelations-graphs

= Relations and Graphs =

A ** relation ** is a set of ordered pairs of values.

A relation can be represented as
 * a list of ordered pairs
 * a table of values
 * a rule
 * a graph

For example, the following are representing the same relation:
 * { (1, –1), (2, 1), (3, 3), (4, 5) }
 * y = 2x – 3 for x Î {1, 2, 3, 4}


 * [[image:04Bgraph1.gif width="226"]]


 * This is an example of a **__discrete__** relationship
 * the independent variable (x) has separate, discrete values
 * A discrete relationship should be shown as individual dots on a graph

For example, the following are representing the same relation:
 * x + y = 3 for x Î R
 * { (0, 3), (1, 2), (2, 1), ... }


 * [[image:04Bgraph2.gif width="226"]]


 * This is an example of a __**continuous**__ relationship
 * the independent variable (x) has a continuous set of possible values
 * A continuous relationship should be shown as a line on a graph
 * the line doesn't have to be a straight line
 * most relationships involve a smoothly curving line


 * Relations and Modelling **

Recall that when graphing a relation
 * the ** independent ** variable
 * changes on its own or is set externally by us
 * should be the first value of the ordered pair
 * should be the top row of the table of values
 * should be on the horizontal axis of the graph
 * can be continuous or discrete


 * The ** dependent ** variable
 * value depends on the value of the other variable
 * should be the second value of the ordered pair
 * should be the bottom row of the table of values
 * should be on the vertical axis of the graph

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