To determine the range of the set of ordered pairs [tex]\(\{(4, 7), (4, -3), (-5, -9)\}\)[/tex], we need to identify all the second elements in these ordered pairs. The range of a set of ordered pairs consists of the second elements (also called the output values) in each pair.
Let’s go through the ordered pairs one by one and identify the second elements:
1. In the ordered pair [tex]\((4, 7)\)[/tex], the second element is [tex]\(7\)[/tex].
2. In the ordered pair [tex]\((4, -3)\)[/tex], the second element is [tex]\(-3\)[/tex].
3. In the ordered pair [tex]\((-5, -9)\)[/tex], the second element is [tex]\(-9\)[/tex].
Thus, the second elements of these ordered pairs are [tex]\(7\)[/tex], [tex]\(-3\)[/tex], and [tex]\(-9\)[/tex].
Therefore, the range is the set of these second elements:
[tex]\[
\{7, -9, -3\}
\][/tex]
So, the correct answer is:
[tex]\(\{7, -9, -3\}\)[/tex].
