Let's analyze the given sets of relations step-by-step.
### Set [tex]\(a = \{(-1, 3), (5, 3), (2, 6), (8, 1)\}\)[/tex]:
1. Domain and Range:
- The domain consists of all the first elements of the ordered pairs: [tex]\(\{-1, 5, 2, 8\}\)[/tex].
- The range consists of all the second elements of the ordered pairs: [tex]\(\{3, 6, 1\}\)[/tex].
2. Is it a function?:
- A relation is a function if every input (first element of each pair) is associated with exactly one output (second element of each pair).
- Here, each input [tex]\(-1, 5, 2, 8\)[/tex] is associated with a unique output.
- Hence, [tex]\(\{(-1, 3), (5, 3), (2, 6), (8, 1)\}\)[/tex] is indeed a function.
### Set [tex]\(b = \{(0, 3), (4, 1), (-2, 4), (4, 5), (-10, 2)\}\)[/tex]:
1. Domain and Range:
- The domain consists of all the first elements of the ordered pairs: [tex]\(\{0, 4, -2, -10\}\)[/tex].
- The range consists of all the second elements of the ordered pairs: [tex]\(\{3, 1, 4, 5, 2\}\)[/tex].
2. Is it a function?:
- Here, the input [tex]\(4\)[/tex] is associated with two different outputs: [tex]\(1\)[/tex] and [tex]\(5\)[/tex].
- Because an input is related to more than one output, [tex]\((4,1)\)[/tex] and [tex]\((4,5)\)[/tex], this relation is not a function.
### Summary of Results:
1. For set [tex]\(a = \{(-1, 3), (5, 3), (2, 6), (8, 1)\}\)[/tex]:
- Domain: [tex]\(\{-1, 5, 2, 8\}\)[/tex]
- Range: [tex]\(\{3, 6, 1\}\)[/tex]
- It is a function.
2. For set [tex]\(b = \{(0, 3), (4, 1), (-2, 4), (4, 5), (-10, 2)\}\)[/tex]:
- Domain: [tex]\(\{0, 4, -2, -10\}\)[/tex]
- Range: [tex]\(\{3, 1, 4, 5, 2\}\)[/tex]
- It is not a function.
