Question
Brian has a set of ordered pairs that represent a function. Which set of coordinates can represent Brian’s ordered pairs?
Group of answer choices
{(9, −4), (3, −3), (2, −2), (9, −8)}
{(7, 2), (5, 9), (5, 10), (−1, 7)}
{(2, 1), (−7, 6), (8, 1), (1, 2)}
{(4, 3), (−1, 5), (5, 3), (−1, 5)}
Group of answer choices
{(9, −4), (3, −3), (2, −2), (9, −8)}
{(7, 2), (5, 9), (5, 10), (−1, 7)}
{(2, 1), (−7, 6), (8, 1), (1, 2)}
{(4, 3), (−1, 5), (5, 3), (−1, 5)}
Answers
GPT-4o mini
To determine which set of coordinates can represent a function, we need to check if any of the x-coordinates (the first elements in the ordered pairs) repeat with different y-coordinates (the second elements). A set of ordered pairs represents a function if each x-coordinate is associated with exactly one y-coordinate.
Let's analyze each set:
1. **{(9, −4), (3, −3), (2, −2), (9, −8)}**
- The x-coordinate 9 appears twice, with different y-coordinates (-4 and -8). This set does not represent a function.
2. **{(7, 2), (5, 9), (5, 10), (−1, 7)}**
- The x-coordinate 5 also appears twice, with different y-coordinates (9 and 10). This set does not represent a function.
3. **{(2, 1), (−7, 6), (8, 1), (1, 2)}**
- All x-coordinates (2, -7, 8, and 1) are unique. This set represents a function.
4. **{(4, 3), (−1, 5), (5, 3), (−1, 5)}**
- The x-coordinate -1 appears twice, but with the same y-coordinate (5 in both cases). This set does represent a function because each x-coordinate is associated with only one y-coordinate.
Based on this analysis, the sets that can represent a function are:
- **{(2, 1), (−7, 6), (8, 1), (1, 2)}**
- **{(4, 3), (−1, 5), (5, 3), (−1, 5)}**
However, since we are looking for a specific choice, the only set that meets the function criteria without repeated x-coordinates is **{(2, 1), (−7, 6), (8, 1), (1, 2)}**.
Let's analyze each set:
1. **{(9, −4), (3, −3), (2, −2), (9, −8)}**
- The x-coordinate 9 appears twice, with different y-coordinates (-4 and -8). This set does not represent a function.
2. **{(7, 2), (5, 9), (5, 10), (−1, 7)}**
- The x-coordinate 5 also appears twice, with different y-coordinates (9 and 10). This set does not represent a function.
3. **{(2, 1), (−7, 6), (8, 1), (1, 2)}**
- All x-coordinates (2, -7, 8, and 1) are unique. This set represents a function.
4. **{(4, 3), (−1, 5), (5, 3), (−1, 5)}**
- The x-coordinate -1 appears twice, but with the same y-coordinate (5 in both cases). This set does represent a function because each x-coordinate is associated with only one y-coordinate.
Based on this analysis, the sets that can represent a function are:
- **{(2, 1), (−7, 6), (8, 1), (1, 2)}**
- **{(4, 3), (−1, 5), (5, 3), (−1, 5)}**
However, since we are looking for a specific choice, the only set that meets the function criteria without repeated x-coordinates is **{(2, 1), (−7, 6), (8, 1), (1, 2)}**.