To determine which of the given sets of ordered pairs represents a function, we need to verify if each input (x-value) in each set maps to exactly one output (y-value).
1. Consider the set [tex]\(\{(-3,-3),(-2,-2),(-1,-1),(0,0),(1,1)\}\)[/tex]:
- Here, each x-value: -3, -2, -1, 0, 1 appears only once and maps to a unique y-value: -3, -2, -1, 0, 1 respectively.
- Therefore, this set does represent a function.
2. Consider the set [tex]\(\{(-3,-3),(-3,-2),(-3,-1),(-3,0),(-4,-1)\}\)[/tex]:
- Here, the x-value -3 appears multiple times and maps to different y-values: -3, -2, -1, 0.
- Therefore, this set does not represent a function.
3. Consider the set [tex]\(\{(-3,-3),(-3,-1),(-1,-2),(-1,-1),(-1,0)\}\)[/tex]:
- Here, the x-values -3 and -1 each appear multiple times, and -3 maps to -3 and -1, and -1 maps to -2, -1, 0.
- Therefore, this set does not represent a function.
4. Consider the set [tex]\(\{(-3,-3),(-3,0),(-1,-3),(0,-3),(-1,-1)\}\)[/tex]:
- Here, the x-values -3 and -1 each appear multiple times, and -3 maps to -3 and 0, and -1 maps to -3 and -1.
- Therefore, this set does not represent a function.
Given the analysis, the only set of ordered pairs that represents a function is:
[tex]\[
\{(-3,-3),(-2,-2),(-1,-1),(0,0),(1,1)\}
\][/tex]
Thus, the correct answer is [tex]\([1]\)[/tex].
