Question

Which of the following functions given in ordered pairs is one-to-one?(1 point)
Responses

{(7,9),(6,4),(1,2),(5,3),(4,1)}
left brace left parenthesis 7 comma 9 right parenthesis comma left parenthesis 6 comma 4 right parenthesis comma left parenthesis 1 comma 2 right parenthesis comma left parenthesis 5 comma 3 right parenthesis comma left parenthesis 4 comma 1 right parenthesis right brace

{(1,3),(4,5),(7,2),(1,5),(4,3)}
left brace left parenthesis 1 comma 3 right parenthesis comma left parenthesis 4 comma 5 right parenthesis comma left parenthesis 7 comma 2 right parenthesis comma left parenthesis 1 comma 5 right parenthesis comma left parenthesis 4 comma 3 right parenthesis right brace

{(2,1),(4,3),(6,3),(8,6),(10,9)}
left brace left parenthesis 2 comma 1 right parenthesis comma left parenthesis 4 comma 3 right parenthesis comma left parenthesis 6 comma 3 right parenthesis comma left parenthesis 8 comma 6 right parenthesis comma left parenthesis 10 comma 9 right parenthesis right brace

{(4,2),(7,3),(10,7),(5,8),(6,2)}

Answer 1

A function is considered one-to-one (or injective) if every output value (y-value) corresponds to exactly one input value (x-value). In other words, no two distinct input values can map to the same output value.

Let's analyze each of the given sets of ordered pairs:

1. **Set 1: {(7,9),(6,4),(1,2),(5,3),(4,1)}**
- Outputs: 9, 4, 2, 3, 1.
- All outputs are unique.
- **This set is one-to-one.**

2. **Set 2: {(1,3),(4,5),(7,2),(1,5),(4,3)}**
- Outputs: 3, 5, 2, 5, 3.
- The outputs 3 and 5 are repeated (1 maps to both 3 and 5, and 4 maps to both 5 and 3).
- **This set is not one-to-one.**

3. **Set 3: {(2,1),(4,3),(6,3),(8,6),(10,9)}**
- Outputs: 1, 3, 3, 6, 9.
- The output 3 is repeated (4 maps to 3 and 6 also maps to 3).
- **This set is not one-to-one.**

4. **Set 4: {(4,2),(7,3),(10,7),(5,8),(6,2)}**
- Outputs: 2, 3, 7, 8, 2.
- The output 2 is repeated (4 maps to 2 and 6 also maps to 2).
- **This set is not one-to-one.**

Based on the analysis, the only one-to-one function among the options provided is:

**Set 1: {(7,9),(6,4),(1,2),(5,3),(4,1)}**.