1.2.1 Relations and Functions Key Objectives
• Identify domain and range for relations. • Determine whether relations are functions. • Use the Vertical Line Test to determine whether a relation is a function. Key Terms
• A relation is a pairing of input values with output values; a set of ordered pairs. • The domain is the set of all possible x -values (inputs) of a relation or function. • The range is the set of all possible y -values (outputs) of a relation or function. • A function is a relation in which there is only one ouput ( y -value) for each input ( x -value). • Vertical Line Test If a vertical line intersects the graph of a relation at only one point, then the relation is a function. If the line intersects the graph of a relation at more than one point, then the relation is not a function. Example 1 Identifying Domain and Range A relation is a pairing of input values with output values. It can be shown as a set of ordered pairs ( x , y ), where x is an input value and y is an output value. The set of all input values for a relation is called the domain, and the set of all output values is called the range.
Example 2 Determining Whether a Relation is a Function
A relation in which the first coordinates is never repeated is called a function. In a function, there is only one output for each input, so each element of the domain is mapped to exactly one element in the range. Although a single input in a function cannot be mapped to more than one output, two or more different inputs can be mapped to the same output.
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