Relations and Functions
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What You'll Learn
… And WhyTo determine whether a relation is a function, as in Examples 2 and 3 |
Identifying Relations and Functions
A relation is a set of ordered pairs. The (age, height) ordered pairs below form a relation.
The domain of a relation is the set of first coordinates of the ordered pairs. The range is the set of second coordinates.
Finding Domain and Range
Find the domain and range of the ordered pairs listed for the giraffe data above.
Key Concepts
Definition Function
A function is a relation that assigns exactly one value in the range to each value in the domain.
One way you can tell whether a relation is a function is to analyze the graph of the relation using the vertical-line test. If any vertical line passes through more than one point of the graph, the relation is not a function.
Using the Vertical-Line Test
Determine whether the relation {(3, 0), (−2, 1), (0, −1), (−3, 2), (3, 2)} is a function.
A line would pass through both (3, 0) and (3, 2), so the relation is not a function.
Another way you can tell whether a relation is a function is by making a mapping diagram. List the domain values and the range values in order. Draw arrows from the domain values to their range values.
Need Help?
In a mapping diagram, functions have no more than one arrow starting from each value of the domain.
Using a Mapping Diagram
Determine whether each relation is a function.
Interactivity Exploring Functions
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