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

Question

Responses

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

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

Answer 1

To determine if a function represented by ordered pairs is one-to-one (injective), we need to ensure that no two different inputs (x-values) produce the same output (y-value).

Let's evaluate each of the sets of ordered pairs you provided:

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

   • Here, the x-value 1 maps to outputs 3 and 5, and the x-value 4 maps to outputs 5 and 3.
   • Since there are repeated x-values (1 and 4) that produce different y-values, this set is not one-to-one.

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

   • The x-value 4 maps to 3, and the x-value 6 also maps to 3.
   • This means multiple x-values map to the same y-value. Thus, this set is not one-to-one.

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

   • Each x-value (7, 6, 1, 5, and 4) produces a unique y-value(9, 4, 2, 3, and 1) with no repetitions.
   • As a result, this set is one-to-one.

Thus, the only one-to-one function among the given sets is the third set: \({(7,9),(6,4),(1,2),(5,3),(4,1)}\).