Answer :
To determine which choice shows a function with a domain of [tex]\(\{-4, -2, 2, 4\}\)[/tex], we need to analyze each set of ordered pairs and extract their domains.
A set of ordered pairs [tex]\((x, y)\)[/tex] represents a function, where [tex]\(x\)[/tex] values are the elements of the domain.
Let's examine each choice step-by-step:
### Choice 1: [tex]\(\{(-4, 2), (-2, 1), (2, 0), (4, 5)\}\)[/tex]
1. Identify the [tex]\(x\)[/tex]-values in each pair:
- First pair: [tex]\((-4, 2)\)[/tex] → [tex]\(x = -4\)[/tex]
- Second pair: [tex]\((-2, 1)\)[/tex] → [tex]\(x = -2\)[/tex]
- Third pair: [tex]\((2, 0)\)[/tex] → [tex]\(x = 2\)[/tex]
- Fourth pair: [tex]\((4, 5)\)[/tex] → [tex]\(x = 4\)[/tex]
2. Combine these [tex]\(x\)[/tex]-values to find the domain:
- Domain of Choice 1: [tex]\(\{-4, -2, 2, 4\}\)[/tex]
### Choice 2: [tex]\(\{(1, -4), (0, -2), (2, 2), (6, 4)\}\)[/tex]
1. Identify the [tex]\(x\)[/tex]-values in each pair:
- First pair: [tex]\((1, -4)\)[/tex] → [tex]\(x = 1\)[/tex]
- Second pair: [tex]\((0, -2)\)[/tex] → [tex]\(x = 0\)[/tex]
- Third pair: [tex]\((2, 2)\)[/tex] → [tex]\(x = 2\)[/tex]
- Fourth pair: [tex]\((6, 4)\)[/tex] → [tex]\(x = 6\)[/tex]
2. Combine these [tex]\(x\)[/tex]-values to find the domain:
- Domain of Choice 2: [tex]\(\{1, 0, 2, 6\}\)[/tex]
### Comparison with Required Domain
The required domain is [tex]\(\{-4, -2, 2, 4\}\)[/tex].
- Domain of Choice 1: [tex]\(\{-4, -2, 2, 4\}\)[/tex]
- Domain of Choice 2: [tex]\(\{1, 0, 2, 6\}\)[/tex]
### Conclusion
Choice 1 has a domain that exactly matches the required domain of [tex]\(\{-4, -2, 2, 4\}\)[/tex]. Therefore, the correct choice is:
[tex]\[ \{(-4, 2), (-2, 1), (2, 0), (4, 5)\} \][/tex]
So, the answer is:
[tex]\[ \boxed{1} \][/tex]
A set of ordered pairs [tex]\((x, y)\)[/tex] represents a function, where [tex]\(x\)[/tex] values are the elements of the domain.
Let's examine each choice step-by-step:
### Choice 1: [tex]\(\{(-4, 2), (-2, 1), (2, 0), (4, 5)\}\)[/tex]
1. Identify the [tex]\(x\)[/tex]-values in each pair:
- First pair: [tex]\((-4, 2)\)[/tex] → [tex]\(x = -4\)[/tex]
- Second pair: [tex]\((-2, 1)\)[/tex] → [tex]\(x = -2\)[/tex]
- Third pair: [tex]\((2, 0)\)[/tex] → [tex]\(x = 2\)[/tex]
- Fourth pair: [tex]\((4, 5)\)[/tex] → [tex]\(x = 4\)[/tex]
2. Combine these [tex]\(x\)[/tex]-values to find the domain:
- Domain of Choice 1: [tex]\(\{-4, -2, 2, 4\}\)[/tex]
### Choice 2: [tex]\(\{(1, -4), (0, -2), (2, 2), (6, 4)\}\)[/tex]
1. Identify the [tex]\(x\)[/tex]-values in each pair:
- First pair: [tex]\((1, -4)\)[/tex] → [tex]\(x = 1\)[/tex]
- Second pair: [tex]\((0, -2)\)[/tex] → [tex]\(x = 0\)[/tex]
- Third pair: [tex]\((2, 2)\)[/tex] → [tex]\(x = 2\)[/tex]
- Fourth pair: [tex]\((6, 4)\)[/tex] → [tex]\(x = 6\)[/tex]
2. Combine these [tex]\(x\)[/tex]-values to find the domain:
- Domain of Choice 2: [tex]\(\{1, 0, 2, 6\}\)[/tex]
### Comparison with Required Domain
The required domain is [tex]\(\{-4, -2, 2, 4\}\)[/tex].
- Domain of Choice 1: [tex]\(\{-4, -2, 2, 4\}\)[/tex]
- Domain of Choice 2: [tex]\(\{1, 0, 2, 6\}\)[/tex]
### Conclusion
Choice 1 has a domain that exactly matches the required domain of [tex]\(\{-4, -2, 2, 4\}\)[/tex]. Therefore, the correct choice is:
[tex]\[ \{(-4, 2), (-2, 1), (2, 0), (4, 5)\} \][/tex]
So, the answer is:
[tex]\[ \boxed{1} \][/tex]
