Question

Dertermine whether the date in the diagram represents a functional relationship, and state the domain and range.1point)

Answer 1

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:

1. **Examine the Diagram:** Check if any x-value (input) is associated with more than one y-value (output).
2. **Identify the Domain:** The set of all possible x-values (inputs).
3. **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.