Question

Find the domain and the range of the relation and determine whether it is a function.
​{(8​,4​),(minus6​,minus3​),(2​,minus1​),(5​,minus6​)}

Answer 1

To analyze the relation \( \{ (8, 4), (-6, -3), (2, -1), (5, -6) \} \), we can identify the domain, range, and determine if it is a function.

1. **Domain**: The domain of a relation is the set of all first elements (or x-coordinates) from the ordered pairs. From the given relation, the first elements are:
- \( 8 \)
- \( -6 \)
- \( 2 \)
- \( 5 \)

Thus, the domain is:
\[
\text{Domain} = \{ 8, -6, 2, 5 \}
\]

2. **Range**: The range of a relation is the set of all second elements (or y-coordinates) from the ordered pairs. From the given relation, the second elements are:
- \( 4 \)
- \( -3 \)
- \( -1 \)
- \( -6 \)

Thus, the range is:
\[
\text{Range} = \{ 4, -3, -1, -6 \}
\]

3. **Function Check**: A relation is a function if each element in the domain is associated with exactly one element in the range. In this relation, each x-coordinate is unique, and no x-coordinate is repeated. Therefore, every element in the domain maps to a single element in the range.

Since there are no repeated x-coordinates, the relation is indeed a function.

In summary:
- **Domain**: \( \{ 8, -6, 2, 5 \} \)
- **Range**: \( \{ 4, -3, -1, -6 \} \)
- **Is it a function?**: Yes, it is a function.