To determine which of the given lists of ordered pairs is a function, we need to recall the definition of a function. A function is a relation where each input (or domain value) is associated with exactly one output (or range value). In other words, no x-value (input) can be repeated with different y-values (outputs).
Let's examine each list of ordered pairs step by step:
### List A: [tex]\((1,2), (4,0), (3,5), (4,3)\)[/tex]
- The x-values are: 1, 4, 3, 4
- The x-value 4 is repeated with different y-values (0 and 3).
Since the x-value 4 is repeated with different y-values, List A is not a function.
### List B: [tex]\((2,5), (3,6), (6,9)\)[/tex]
- The x-values are: 2, 3, 6
- None of the x-values are repeated.
Since none of the x-values are repeated, List B is a function.
### List C: [tex]\((2,5), (3,6), (2,1)\)[/tex]
- The x-values are: 2, 3, 2
- The x-value 2 is repeated with different y-values (5 and 1).
Since the x-value 2 is repeated with different y-values, List C is not a function.
### List D: [tex]\((-1,2), (2,3), (3,1), (2,5)\)[/tex]
- The x-values are: -1, 2, 3, 2
- The x-value 2 is repeated with different y-values (3 and 5).
Since the x-value 2 is repeated with different y-values, List D is not a function.
### Conclusion
After examining each list, List B was determined to be the only one where none of the x-values are repeated with different y-values. Therefore, List B:
[tex]\((2,5), (3,6), (6,9)\)[/tex]
is a function. The results are:
- List A: Not a function
- List B: Function
- List C: Not a function
- List D: Not a function
Thus, List B is the answer.
