Example: Finding the Domain and Range of the Relation
To find the domain and range of the relation , we analyze the first and second coordinates of each ordered pair. The domain is the set of all the -values. Extracting the first coordinate from each pair yields the domain: . The range is the set of all the -values. Extracting the second coordinate from each pair gives the range: .
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Example: Sets of Ordered Pairs as a Mathematical Function
Example: Sets of Ordered Pairs Not Representing a Mathematical Function
Example: Finding the Domain and Range of the Relation
Example: Finding the Domain and Range of the Relation
Example: Finding the Domain and Range of the Relation
A warehouse manager records the aisle number and the total number of pallets stored in that aisle as a set of ordered pairs: . Which of the following sets represents the domain of this relation?
An IT technician logs the number of help desk tickets resolved and the hours spent working on them as a set of ordered pairs: . The domain of this relation is the set .
A retail manager tracks the number of hours a part-time employee works () and their total weekly earnings in dollars (). The data for three weeks is recorded as the following set of ordered pairs: . Match each mathematical term with the correct set representing that part of the relation.
Defining and Identifying the Range in Payroll Data
A training coordinator tracks the number of professional development modules an employee completes () and the total time spent in hours () as a set of ordered pairs: . In this mathematical relation, the set of all -values, , is known as the ____.
Learn After
A company's training dashboard records the number of hours an employee spends in a simulator () and their resulting performance score (). For five employees, this data forms the relation . Recalling how to extract values from ordered pairs, what are the domain and range of this relation?
An inventory tracking system at a regional distribution center assigns a unique shelf identification number () to each shelving unit and records the total number of stock units () currently stored on that shelf. For a specific aisle, the data is represented by the relation R = \left\{ (1,1), (2,4), (3,9), (4,16), (5,25) ight\}. Match each mathematical term to the correct set derived from this inventory data.
A network engineer is monitoring data traffic and records the relationship between the number of active users () and the total bandwidth usage in megabits per second (). The resulting relation is . True or False: The domain of this relation is the set .
Logistics Throughput Range Identification
A maintenance supervisor at a production facility uses the relation to track the number of machines serviced () and the total time spent in hours (). In this mathematical relation, the set of all first coordinates, , is known as the ____ of the relation.