Alright! Let's delve into how we can determine the domain and range of the given set of ordered pairs: [tex]\(\{(19,12),(11,5),(2,2),(-4,16),(6,5),(-2,1),(3,-3)\}\)[/tex].
### Domain:
The domain of a set of ordered pairs is the set of all the first elements (or x-coordinates) from each pair. Here's the step-by-step extraction of these first elements from the given pairs:
1. From [tex]\((19, 12)\)[/tex], the first element is [tex]\(19\)[/tex].
2. From [tex]\((11, 5)\)[/tex], the first element is [tex]\(11\)[/tex].
3. From [tex]\((2, 2)\)[/tex], the first element is [tex]\(2\)[/tex].
4. From [tex]\((-4, 16)\)[/tex], the first element is [tex]\(-4\)[/tex].
5. From [tex]\((6, 5)\)[/tex], the first element is [tex]\(6\)[/tex].
6. From [tex]\((-2, 1)\)[/tex], the first element is [tex]\(-2\)[/tex].
7. From [tex]\((3, -3)\)[/tex], the first element is [tex]\(3\)[/tex].
Now, putting all these first elements together, we get:
[tex]\[ \{19, 11, 2, -4, 6, -2, 3\} \][/tex]
Therefore, the domain is:
[tex]\[ \boxed{\{19, 11, 2, -4, 6, -2, 3\}} \][/tex]
### Range:
The range of a set of ordered pairs is the set of all the second elements (or y-coordinates) from each pair. Here's the step-by-step extraction of these second elements:
1. From [tex]\((19, 12)\)[/tex], the second element is [tex]\(12\)[/tex].
2. From [tex]\((11, 5)\)[/tex], the second element is [tex]\(5\)[/tex].
3. From [tex]\((2, 2)\)[/tex], the second element is [tex]\(2\)[/tex].
4. From [tex]\((-4, 16)\)[/tex], the second element is [tex]\(16\)[/tex].
5. From [tex]\((6, 5)\)[/tex], the second element is [tex]\(5\)[/tex].
6. From [tex]\((-2, 1)\)[/tex], the second element is [tex]\(1\)[/tex].
7. From [tex]\((3, -3)\)[/tex], the second element is [tex]\(-3\)[/tex].
Now, putting all these second elements together, we get:
[tex]\[ \{12, 5, 2, 16, 1, -3\} \][/tex]
(Note that the element [tex]\(5\)[/tex] appears twice, but sets contain only distinct elements).
Therefore, the range is:
[tex]\[ \boxed{\{12, 5, 2, 16, 1, -3\}} \][/tex]
To summarize, for the given set of ordered pairs [tex]\(\{(19,12), (11,5), (2,2), (-4,16), (6,5), (-2,1), (3,-3)\}\)[/tex],
- The Domain is: [tex]\(\boxed{\{19, 11, 2, -4, 6, -2, 3\}}\)[/tex]
- The Range is: [tex]\(\boxed{\{12, 5, 2, 16, 1, -3\}}\)[/tex]
