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

Question

Responses

{(4,2),(7,3),(10,7),(5,8),(6,2)}
left brace left parenthesis 4 comma 2 right parenthesis comma left parenthesis 7 comma 3 right parenthesis comma left parenthesis 10 comma 7 right parenthesis comma left parenthesis 5 comma 8 right parenthesis comma left parenthesis 6 comma 2 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

{(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

{(2,1),(4,3),(6,3),(8,6),(10,9)}

Answer 1

To determine whether each set of ordered pairs represents a one-to-one function, we need to check if each input (the first element in each pair) maps to a unique output (the second element in each pair). In other words, no two different inputs should produce the same output.

Let's analyze each option:

1. {(4,2),(7,3),(10,7),(5,8),(6,2)}

   • Outputs: 2, 3, 7, 8.
   • Input 4 maps to 2 and input 6 also maps to 2.
   • Not one-to-one.

2. {(1,3),(4,5),(7,2),(1,5),(4,3)}

   • Outputs: 3, 5, 2.
   • Input 1 maps to both 3 and 5, and input 4 maps to both 5 and 3.
   • Not one-to-one.

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

   • Outputs: 9, 4, 2, 3, 1.
   • Each input maps to a unique output.
   • One-to-one.

4. {(2,1),(4,3),(6,3),(8,6),(10,9)}

   • Outputs: 1, 3, 6, 9.
   • Input 4 maps to 3 and input 6 also maps to 3.
   • Not one-to-one.

The only one-to-one function among the given options is:

{(7,9),(6,4),(1,2),(5,3),(4,1)}