To determine if each set of ordered pairs represents a function, we need to check if every input (or x-value) is associated with exactly one output (or y-value). This means no x-value should repeat with a different y-value.
Let's analyze each set of ordered pairs one by one:
1. [tex]\((2, 3), (6, -5), (-1, 3)\)[/tex]
- Check the x-values: 2, 6, -1
- None of these x-values repeat.
- Since each x-value is unique, this set of ordered pairs represents a function.
2. [tex]\((1, 9), (-3, -2), (1, -4)\)[/tex]
- Check the x-values: 1, -3, 1
- The x-value 1 repeats, with different y-values (9 and -4).
- Since there is a repeated x-value with different y-values, this set does not represent a function.
3. [tex]\((7, -4), (0, 9), (2, -2)\)[/tex]
- Check the x-values: 7, 0, 2
- None of these x-values repeat.
- Since each x-value is unique, this set of ordered pairs represents a function.
4. [tex]\((0, 3), (0, 7), (4, 0)\)[/tex]
- Check the x-values: 0, 0, 4
- The x-value 0 repeats, with different y-values (3 and 7).
- Since there is a repeated x-value with different y-values, this set does not represent a function.
5. [tex]\((-6, 5), (-5, 6), (8, 2)\)[/tex]
- Check the x-values: -6, -5, 8
- None of these x-values repeat.
- Since each x-value is unique, this set of ordered pairs represents a function.
Summarizing the results:
1. [tex]\((2, 3), (6, -5), (-1, 3)\)[/tex] - Function
2. [tex]\((1, 9), (-3, -2), (1, -4)\)[/tex] - Not a Function
3. [tex]\((7, -4), (0, 9), (2, -2)\)[/tex] - Function
4. [tex]\((0, 3), (0, 7), (4, 0)\)[/tex] - Not a Function
5. [tex]\((-6, 5), (-5, 6), (8, 2)\)[/tex] - Function
