Answer :
To determine which of the given sets of ordered pairs is not a function, we need to understand the definition of a function. A relation (set of ordered pairs) is a function if and only if every input (x-value) corresponds to exactly one output (y-value). In other words, no x-value should repeat within a set.
Let's analyze each set of ordered pairs to check if they are functions:
### Set 1: [tex]\(\{(-6,4), (-3,-2), (0,5), (1,-2), (2,3)\}\)[/tex]
- Check if any x-values repeat.
- x-values: -6, -3, 0, 1, 2
- All x-values are unique.
- Conclusion: This is a function.
### Set 2: [tex]\(\{(-8,3), (-6,5), (-4,2), (-2,7), (-1,4)\}\)[/tex]
- Check if any x-values repeat.
- x-values: -8, -6, -4, -2, -1
- All x-values are unique.
- Conclusion: This is a function.
### Set 3: [tex]\(\{(-4,-2), (-1,-1), (-1,1), (3,5), (7,10)\}\)[/tex]
- Check if any x-values repeat.
- x-values: -4, -1, -1, 3, 7
- The x-value -1 repeats with different y-values: (-1,-1) and (-1,1)
- Conclusion: This is not a function because the x-value -1 maps to two different y-values.
### Set 4: [tex]\(\{(5,0), (4,0), (3,0), (2,0), (1,0)\}\)[/tex]
- Check if any x-values repeat.
- x-values: 5, 4, 3, 2, 1
- All x-values are unique.
- Conclusion: This is a function.
Since the third set [tex]\(\{(-4,-2), (-1,-1), (-1,1), (3,5), (7,10)\}\)[/tex] contains a repeated x-value with different y-values for the x-value -1, this set is not a function.
Final Answer:
The set [tex]\(\{(-4,-2), (-1,-1), (-1,1), (3,5), (7,10)\}\)[/tex] is not a function, and it is the third set. Therefore, the third set of ordered pairs is not a function.
Let's analyze each set of ordered pairs to check if they are functions:
### Set 1: [tex]\(\{(-6,4), (-3,-2), (0,5), (1,-2), (2,3)\}\)[/tex]
- Check if any x-values repeat.
- x-values: -6, -3, 0, 1, 2
- All x-values are unique.
- Conclusion: This is a function.
### Set 2: [tex]\(\{(-8,3), (-6,5), (-4,2), (-2,7), (-1,4)\}\)[/tex]
- Check if any x-values repeat.
- x-values: -8, -6, -4, -2, -1
- All x-values are unique.
- Conclusion: This is a function.
### Set 3: [tex]\(\{(-4,-2), (-1,-1), (-1,1), (3,5), (7,10)\}\)[/tex]
- Check if any x-values repeat.
- x-values: -4, -1, -1, 3, 7
- The x-value -1 repeats with different y-values: (-1,-1) and (-1,1)
- Conclusion: This is not a function because the x-value -1 maps to two different y-values.
### Set 4: [tex]\(\{(5,0), (4,0), (3,0), (2,0), (1,0)\}\)[/tex]
- Check if any x-values repeat.
- x-values: 5, 4, 3, 2, 1
- All x-values are unique.
- Conclusion: This is a function.
Since the third set [tex]\(\{(-4,-2), (-1,-1), (-1,1), (3,5), (7,10)\}\)[/tex] contains a repeated x-value with different y-values for the x-value -1, this set is not a function.
Final Answer:
The set [tex]\(\{(-4,-2), (-1,-1), (-1,1), (3,5), (7,10)\}\)[/tex] is not a function, and it is the third set. Therefore, the third set of ordered pairs is not a function.
