Question
Which relation is a function?
Responses
{(4, 2), (3, 3), (2, 4), (3, 2)}
left bracket ordered pair 4 comma 2 end ordered pair comma ordered pair 3 comma 3 end ordered pair comma ordered pair 2 comma 4 end ordered pair comma ordered pair 3 comma 2 end ordered pair right bracket
{(1, −1), (−2, 2), (−1, 2), (1, −2)}
left bracket begin ordered pair 1 comma negative 1 end ordered pair, begin ordered pair negative 2 comma 2 end ordered pair, begin ordered pair negative comma 2 end ordered pair, begin ordered pair 1 comma negative 2 end ordered pair
{(1, 4), (2, 3), (3, 2), (4, 1)}
left bracket begin ordered pair 1 comma 4 end ordered pair comma begin ordered pair 2 comma 3 end ordered pair comma begin ordered pair 3 comma 2 end ordered pair comma begin ordered pair 4 comma 1 end ordered pair right bracket
{(1, 2), (2, 3), (3, 2), (2, 1)}
left bracket ordered pair 1 comma 2 end ordered pair comma ordered pair 2 comma 3 end ordered pair comma ordered pair 3 comma 2 end ordered pair ordered pair 2 comma 1 end ordered pair right bracket
Responses
{(4, 2), (3, 3), (2, 4), (3, 2)}
left bracket ordered pair 4 comma 2 end ordered pair comma ordered pair 3 comma 3 end ordered pair comma ordered pair 2 comma 4 end ordered pair comma ordered pair 3 comma 2 end ordered pair right bracket
{(1, −1), (−2, 2), (−1, 2), (1, −2)}
left bracket begin ordered pair 1 comma negative 1 end ordered pair, begin ordered pair negative 2 comma 2 end ordered pair, begin ordered pair negative comma 2 end ordered pair, begin ordered pair 1 comma negative 2 end ordered pair
{(1, 4), (2, 3), (3, 2), (4, 1)}
left bracket begin ordered pair 1 comma 4 end ordered pair comma begin ordered pair 2 comma 3 end ordered pair comma begin ordered pair 3 comma 2 end ordered pair comma begin ordered pair 4 comma 1 end ordered pair right bracket
{(1, 2), (2, 3), (3, 2), (2, 1)}
left bracket ordered pair 1 comma 2 end ordered pair comma ordered pair 2 comma 3 end ordered pair comma ordered pair 3 comma 2 end ordered pair ordered pair 2 comma 1 end ordered pair right bracket
Answers
GPT-4o mini
To determine which of the given relations is a function, we need to check if each input (the first element of the ordered pair) corresponds to exactly one output (the second element of the ordered pair). In other words, for a relation to be a function, there should be no two ordered pairs with the same first element and different second elements.
Let's evaluate each relation:
1. **Relation 1:** \({(4, 2), (3, 3), (2, 4), (3, 2)}\)
- Here, the input "3" corresponds to two different outputs (3 and 2).
- **Not a function.**
2. **Relation 2:** \({(1, -1), (-2, 2), (-1, 2), (1, -2)}\)
- The input "1" corresponds to two different outputs (-1 and -2).
- **Not a function.**
3. **Relation 3:** \({(1, 4), (2, 3), (3, 2), (4, 1)}\)
- Each input (1, 2, 3, and 4) has a unique output.
- **This is a function.**
4. **Relation 4:** \({(1, 2), (2, 3), (3, 2), (2, 1)}\)
- The input "2" corresponds to two different outputs (3 and 1).
- **Not a function.**
Based on the evaluations, the relation that is a function is:
**Relation 3:** \({(1, 4), (2, 3), (3, 2), (4, 1)}\)
Let's evaluate each relation:
1. **Relation 1:** \({(4, 2), (3, 3), (2, 4), (3, 2)}\)
- Here, the input "3" corresponds to two different outputs (3 and 2).
- **Not a function.**
2. **Relation 2:** \({(1, -1), (-2, 2), (-1, 2), (1, -2)}\)
- The input "1" corresponds to two different outputs (-1 and -2).
- **Not a function.**
3. **Relation 3:** \({(1, 4), (2, 3), (3, 2), (4, 1)}\)
- Each input (1, 2, 3, and 4) has a unique output.
- **This is a function.**
4. **Relation 4:** \({(1, 2), (2, 3), (3, 2), (2, 1)}\)
- The input "2" corresponds to two different outputs (3 and 1).
- **Not a function.**
Based on the evaluations, the relation that is a function is:
**Relation 3:** \({(1, 4), (2, 3), (3, 2), (4, 1)}\)