To determine which set of ordered pairs represents a function, we must check whether each set satisfies the definition of a function. Specifically, a set of ordered pairs is a function if each input (x-value) maps to exactly one output (y-value). This means that for each unique x-value, there must be only one corresponding y-value.
Let's examine each set closely:
1. Set 1: [tex]\(\{(3,2),(4,4),(6,3),(4,5)\}\)[/tex]
- The x-values are: [tex]\(3, 4, 6, 4\)[/tex].
- Notice that [tex]\(4\)[/tex] appears twice but maps to different y-values ([tex]\(4\)[/tex] and [tex]\(5\)[/tex]).
- Therefore, Set 1 does not represent a function.
2. Set 2: [tex]\(\{(4,-3),(4,-1),(4,3),(4,6)\}\)[/tex]
- The x-values are: [tex]\(4, 4, 4, 4\)[/tex].
- All x-values are the same but map to different y-values ([tex]\(-3, -1, 3, 6\)[/tex]).
- Consequently, Set 2 does not represent a function.
3. Set 3: [tex]\(\{(-4,4),(-2,4),(1,4),(5,4)\}\)[/tex]
- The x-values are: [tex]\(-4, -2, 1, 5\)[/tex].
- Each x-value is unique and maps to one y-value ([tex]\(4\)[/tex]).
- This satisfies the definition of a function.
- Therefore, Set 3 represents a function.
4. Set 4: [tex]\(\{(-3,-3),(-2,-4),(-2,-1),(-1,-5)\}\)[/tex]
- The x-values are: [tex]\(-3, -2, -2, -1\)[/tex].
- Notice that [tex]\(-2\)[/tex] appears twice but maps to different y-values ([tex]\(-4\)[/tex] and [tex]\(-1\)[/tex]).
- Thus, Set 4 does not represent a function.
After evaluating all the sets of ordered pairs, we conclude that:
- Set 3: [tex]\(\{(-4,4),(-2,4),(1,4),(5,4)\}\)[/tex] is the set that represents a function.
So, the set of ordered pairs that represents a function is [tex]\(\{(-4,4),(-2,4),(1,4),(5,4)\}\)[/tex].
