4a+-+Introduction+to+functions,+Domain,+Range

__Functions and Equations of lines.__

http://www.purplemath.com/modules/fcns2.htm http://mathforum.org/library/drmath/sets/select/dm_domain_range.html
 * Links that may help**:

__Introduction to Functions:__ On the coordinate plane, every ordered pair is dependent on each other. The y depends on the value of the x. The **y variable** is called the dependent variable and the **x variable** is called the independent variable.

A **relation** is a connection between inputs and outputs

Ways that relations can be expressed: //mapping diagram, graph, table, equation//


 * Domain** : is the input of a relation. It is the set of all inputs
 * Range** : is the output of a relation. It is a set of all outputs.

//For example//: J = { (2,1), (4,-1), (3,2)}

Domain = { 2, 4, 3} and Range = { 1, -1, }
 * keep in mind there are no repeated numbers.

//To graph a relation//: If you are given 3 sets of x,y coordinates, graph them as you would separately

//Mapping:// To make a mapping diagram, make one bubble for the x input and one for the y output. Put each set of x's in the x input and every y in the y output. However, remember not to repeat any numbers. Connect each input to exactly one output.

//Table of Values:// This is similar to the mapping diagram but instead, it is a table. Label one row input for the x and the other output for the y.

//Equations:// Test each point to verify that this rule connects each input of relation to its appropriate output.


 * Function -** connects each input to exactly one output.

After graphing/mapping/making a table/solving an equation, if there are same x's with 2 y's, it means it is NOT a function. A helpful hint for graphs, is the **vertical line test**: when you take a vertical line and you run it across the graph, it if hits at more than one time, it is NOT a function.

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