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Suppose that the relation \( S \) is defined as follows:

[tex]\[ S = \{(9,2), (-6,2), (-2,-6)\} \][/tex]

Give the domain and range of \( S \). Write your answers using set notation.

[tex]\[ \text{domain} = \square \][/tex]
[tex]\[ \text{range} = \square \][/tex]

Sagot :

GinnyAnswer
To find the domain and range of the given relation \( S = \{(9, 2), (-6, 2), (-2, -6)\} \):

1. Domain:
- The domain of a relation is the set of all first elements (x-values) from the ordered pairs.
- From the pairs \((9, 2)\), \((-6, 2)\), and \((-2, -6)\), the first elements are \(9\), \(-6\), and \(-2\).
- Therefore, the domain is the set of these first elements.

[tex]\[ \text{domain} = \{9, -6, -2\} \][/tex]

2. Range:
- The range of a relation is the set of all second elements (y-values) from the ordered pairs.
- From the pairs \((9, 2)\), \((-6, 2)\), and \((-2, -6)\), the second elements are \(2\), \(2\), and \(-6\).
- However, in a set, we do not list duplicate elements. So, we only need one instance of each unique second element.

[tex]\[ \text{range} = \{2, -6\} \][/tex]

Therefore, the domain and range of the relation \( S \) are:

[tex]\[ \text{domain} = \{9, -6, -2\} \][/tex]
[tex]\[ \text{range} = \{2, -6\} \][/tex]
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