Let's determine the range of the given relation described by the set of ordered pairs [tex]\(\{(-2,0),(-1,2),(0,1),(4,9),(5,-3)\}\)[/tex].
The range of a relation is the set of all second elements (or y-values) from each ordered pair in the relation. To find the range, follow these steps:
1. List the y-values from each ordered pair:
- From [tex]\((-2, 0)\)[/tex], the y-value is [tex]\(0\)[/tex].
- From [tex]\((-1, 2)\)[/tex], the y-value is [tex]\(2\)[/tex].
- From [tex]\((0, 1)\)[/tex], the y-value is [tex]\(1\)[/tex].
- From [tex]\((4, 9)\)[/tex], the y-value is [tex]\(9\)[/tex].
- From [tex]\((5, -3)\)[/tex], the y-value is [tex]\(-3\)[/tex].
2. Collect all these y-values together:
- The y-values are [tex]\([0, 2, 1, 9, -3]\)[/tex].
3. Remove any duplicate values to ensure all elements are unique (although there are no duplicates in this list).
4. Sort the y-values in ascending order to better understand the range:
- The sorted y-values are [tex]\([-3, 0, 1, 2, 9]\)[/tex].
Therefore, the range of the relation described by the set of ordered pairs [tex]\(\{(-2,0),(-1,2),(0,1),(4,9),(5,-3)\}\)[/tex] is [tex]\(\{-3, 0, 1, 2, 9\}\)[/tex].
Now, identify the correct choice from the given options:
- [tex]\(\{-2, -1, 4, 5, 9\}\)[/tex]
- [tex]\(\{-3, 0, 1, 2, 9\}\)[/tex]
- [tex]\(\{-2, -1, 0, 4, 5\}\)[/tex]
- [tex]\(\{-3, -2, -1, 0, 4\}\)[/tex]
The correct option is:
[tex]\(\{-3, 0, 1, 2, 9\}\)[/tex].
