To determine if each set of ordered pairs represents a function, we need to check whether each element of the first component (x-value) appears only once. A set of ordered pairs is a function if each x-value is unique. Let's check each set of ordered pairs one by one:
1. Set 1: [tex]\((2, 3), (6, -5), (-1, 3)\)[/tex]
- The x-values are: [tex]\([2, 6, -1]\)[/tex]
- All x-values are unique.
- Result: Function - [tex]\(1\)[/tex]
2. Set 2: [tex]\((1, 9), (-3, -2), (1, -4)\)[/tex]
- The x-values are: [tex]\([1, -3, 1]\)[/tex]
- The x-value [tex]\(1\)[/tex] appears more than once.
- Result: Not a Function - [tex]\(0\)[/tex]
3. Set 3: [tex]\((7, -4), (0, 9), (2, -2)\)[/tex]
- The x-values are: [tex]\([7, 0, 2]\)[/tex]
- All x-values are unique.
- Result: Function - [tex]\(1\)[/tex]
4. Set 4: [tex]\((0, 3), (0, 7), (4, 0)\)[/tex]
- The x-values are: [tex]\([0, 0, 4]\)[/tex]
- The x-value [tex]\(0\)[/tex] appears more than once.
- Result: Not a Function - [tex]\(0\)[/tex]
5. Set 5: [tex]\((-6, 5), (-5, 6), (8, 2)\)[/tex]
- The x-values are: [tex]\([-6, -5, 8]\)[/tex]
- All x-values are unique.
- Result: Function - [tex]\(1\)[/tex]
Combining all the results, we get:
[tex]\((1, 0, 1, 0, 1)\)[/tex]
So, the final classification is:
- [tex]\((2, 3), (6, -5), (-1, 3)\)[/tex] -> Function (1)
- [tex]\((1, 9), (-3, -2), (1, -4)\)[/tex] -> Not a Function (0)
- [tex]\((7, -4), (0, 9), (2, -2)\)[/tex] -> Function (1)
- [tex]\((0, 3), (0, 7), (4, 0)\)[/tex] -> Not a Function (0)
- [tex]\((-6, 5), (-5, 6), (8, 2)\)[/tex] -> Function (1)
