Answer :
To determine which of the given sets of ordered pairs represent a function, we need to recall the definition of a function in the context of relations. A relation is a function if every input (i.e., the first element in the pair) is related to exactly one output (i.e., the second element in the pair).
Let's analyze each set one by one:
1. \(\{(1, -3), (1, -1), (1, 1), (1, 3), (1, 5)\}\)
- In this set, the first element (input) is always 1, but it corresponds to multiple different outputs: -3, -1, 1, 3, and 5.
- Since one input (1) maps to multiple outputs, this set of pairs is not a function.
2. \(\{(-2, 5), (7, 5), (-4, 0), (3, 1), (0, -6)\}\)
- In this set, each input is unique and corresponds to exactly one output.
- Specifically, -2 maps to 5, 7 maps to 5, -4 maps to 0, 3 maps to 1, and 0 maps to -6.
- Since every input is associated with one and only one output, this set of pairs is a function.
3. \(\{(1, 2), (2, 3), (3, 4), (2, 1), (1, 0)\}\)
- In this set, the input 1 maps to both 2 and 0, and the input 2 maps to both 3 and 1.
- Since there are inputs that correspond to multiple outputs, this set of pairs is not a function.
4. \(\{(2, -8), (6, 4), (-3, 9), (2, 0), (-5, 3)\}\)
- In this set, the input 2 maps to both -8 and 0.
- Since an input (2) maps to multiple outputs, this set of pairs is not a function.
To summarize, only the second set [tex]\(\{(-2, 5), (7, 5), (-4, 0), (3, 1), (0, -6)\}\)[/tex] is a function. The other sets do not meet the criteria for being a function because they have at least one input that maps to multiple outputs.
Let's analyze each set one by one:
1. \(\{(1, -3), (1, -1), (1, 1), (1, 3), (1, 5)\}\)
- In this set, the first element (input) is always 1, but it corresponds to multiple different outputs: -3, -1, 1, 3, and 5.
- Since one input (1) maps to multiple outputs, this set of pairs is not a function.
2. \(\{(-2, 5), (7, 5), (-4, 0), (3, 1), (0, -6)\}\)
- In this set, each input is unique and corresponds to exactly one output.
- Specifically, -2 maps to 5, 7 maps to 5, -4 maps to 0, 3 maps to 1, and 0 maps to -6.
- Since every input is associated with one and only one output, this set of pairs is a function.
3. \(\{(1, 2), (2, 3), (3, 4), (2, 1), (1, 0)\}\)
- In this set, the input 1 maps to both 2 and 0, and the input 2 maps to both 3 and 1.
- Since there are inputs that correspond to multiple outputs, this set of pairs is not a function.
4. \(\{(2, -8), (6, 4), (-3, 9), (2, 0), (-5, 3)\}\)
- In this set, the input 2 maps to both -8 and 0.
- Since an input (2) maps to multiple outputs, this set of pairs is not a function.
To summarize, only the second set [tex]\(\{(-2, 5), (7, 5), (-4, 0), (3, 1), (0, -6)\}\)[/tex] is a function. The other sets do not meet the criteria for being a function because they have at least one input that maps to multiple outputs.
