To determine whether a date in a diagram represents a functional relationship, we need to assess whether each input (usually represented on the x-axis) corresponds to exactly one output (represented on the y-axis).
A relation is considered functional if no two ordered pairs have the same first element but different second elements.
Here’s how you can evaluate a functional relationship:
- Examine the Diagram: Check if any x-value (input) is associated with more than one y-value (output).
- Identify the Domain: The set of all possible x-values (inputs).
- Identify the Range: The set of all possible y-values (outputs).
Example:
If you had a set of ordered pairs like this:
- (1, 2)
- (2, 3)
- (1, 4)
The first element of the first and third pairs (1) has two corresponding values (2 and 4). Therefore, this relation is not functional.
If instead your ordered pairs were:
- (1, 2)
- (2, 3)
- (3, 4)
Here, each input corresponds to exactly one output. Thus, this relation is functional.
Domain and Range:
Using the functional example above:
- Domain: {1, 2, 3}
- Range: {2, 3, 4}
Please provide the specific ordered pairs or a description of the diagram so I can give you a precise answer regarding the functional relationship, as well as the domain and range.
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