Question

Which of the following relations is a one-to-one function?(1 point) Responses {(−3,−2),(3,4),(−1,−2),(−1,5)} start set open paren negative 3 comma negative 2 close paren comma open paren 3 comma 4 close paren comma open paren negative 1 comma negative 2 close paren comma open paren negative 1 comma 5 close paren end set {(1,2),(1,4),(1,5),(1,6)} start set open paren 1 comma 2 close paren comma open paren 1 comma 4 close paren comma open paren 1 comma 5 close paren comma open paren 1 comma 6 close paren end set {(4,−5),(3,−5),(2,8),(1,8)} start set open paren 4 comma negative 5 close paren comma open paren 3 comma negative 5 close paren comma open paren 2 comma 8 close paren comma open paren 1 comma 8 close paren end set {(10,9),(8,7),(6,5),(4,3)}

explain how do you know?

Answer 1

To determine if a relation is a one-to-one function, we need to check if each input (or x-value) corresponds to exactly one unique output (or y-value), and different inputs must map to different outputs.

1. **Relation**: {(-3, -2), (3, 4), (-1, -2), (-1, 5)}
- **Check**: The x-value -1 is associated with two different y-values: -2 and 5.
- **Conclusion**: Not a one-to-one function.

2. **Relation**: {(1, 2), (1, 4), (1, 5), (1, 6)}
- **Check**: The x-value 1 is associated with multiple y-values: 2, 4, 5, and 6.
- **Conclusion**: Not a one-to-one function.

3. **Relation**: {(4, -5), (3, -5), (2, 8), (1, 8)}
- **Check**: The y-value -5 is associated with the x-values 4 and 3, and the y-value 8 is associated with x-values 2 and 1.
- **Conclusion**: Not a one-to-one function.

4. **Relation**: {(10, 9), (8, 7), (6, 5), (4, 3)}
- **Check**: Each x-value (10, 8, 6, and 4) corresponds to a unique y-value (9, 7, 5, and 3), and all x-values are distinct.
- **Conclusion**: This is a one-to-one function.

### Summary:
The only relation that is a one-to-one function is **{(10, 9), (8, 7), (6, 5), (4, 3)}**, as each input has exactly one unique output, and different inputs correspond to different outputs.