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Which of the relations given by the following sets of ordered pairs is not a function?

A. [tex]\{(-6,4),(-3,-2),(0,5),(1,-2),(2,3)\}[/tex]
B. [tex]\{(-8,3),(-6,5),(-4,2),(-2,7),(-1,4)\}[/tex]
C. [tex]\{(-4,-2),(-1,-1),(-1,1),(3,5),(7,10)\}[/tex]
D. [tex]\{(5,0),(4,0),(3,0),(2,0),(1,0)\}[/tex]

Sagot :

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.