Reese Boyd
08/28/2023 · High School
Suppose that the relation \( S \) is defined as follows. \[ S=\{(-8,-9),(3,7),(3,-7)\} \] Give the domain and range of \( S \). Write your answers using set notation.
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Step-by-step Solution
The domain of a relation is the set of all first elements (or inputs) of the ordered pairs, while the range is the set of all second elements (or outputs).
For the relation \( S = \{(-8,-9), (3,7), (3,-7)\} \):
- The first elements (domain) are: \(-8\) and \(3\).
- The second elements (range) are: \(-9\), \(7\), and \(-7\).
Now, we can express the domain and range in set notation:
- The domain of \( S \) is:
\[
\text{Domain}(S) = \{-8, 3\}
\]
- The range of \( S \) is:
\[
\text{Range}(S) = \{-9, 7, -7\}
\]
Thus, the final answers are:
\[
\text{Domain}(S) = \{-8, 3\}
\]
\[
\text{Range}(S) = \{-9, 7, -7\}
\]
Quick Answer
\[
\text{Domain}(S) = \{-8, 3\}
\]
\[
\text{Range}(S) = \{-9, 7, -7\}
\]
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