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

{(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

{(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

{(10,9),(8,7),(6,5),(4,3)}

Answer 1

To determine which of the given relations is a one-to-one function, we need to check if each input (or first element of the ordered pairs) is associated with exactly one unique output (or second element). A function is one-to-one if no two different inputs produce the same output.

Let's analyze each relation:

1. **Relation: {(-3,-2), (3,4), (-1,-2), (-1,5)}**
- Here, the input `-1` is associated with two different outputs: `-2` and `5`.
- **Not one-to-one.**

2. **Relation: {(4,-5), (3,-5), (2,8), (1,8)}**
- The inputs `3` and `4` both map to `-5`, and the inputs `1` and `2` both map to `8`.
- **Not one-to-one.**

3. **Relation: {(1,2), (1,4), (1,5), (1,6)}**
- Here, the input `1` is associated with multiple outputs: `2`, `4`, `5`, and `6`.
- **Not one-to-one.**

4. **Relation: {(10,9), (8,7), (6,5), (4,3)}**
- Each input (10, 8, 6, 4) is associated with a unique output (9, 7, 5, 3), with no repetitions.
- **One-to-one.**

Thus, the only relation that is a one-to-one function is: **{(10,9), (8,7), (6,5), (4,3)}**.