To determine whether the given relation is a function, we need to check if each domain value (the first element of each ordered pair) is associated with exactly one range value (the second element of each ordered pair). The relation provided is:
[tex]\[ \{(-3, -2), (-1, 0), (1, 0), (5, -2)\} \][/tex]
1. First, let's list the domain and range of the relation:
- Domain (first elements): [tex]\(\{-3, -1, 1, 5\}\)[/tex]
- Range (second elements): [tex]\(\{-2, 0, 0, -2\}\)[/tex]
2. Next, let's check if any domain value repeats:
- Domain values: [tex]\(-3, -1, 1, 5\)[/tex]
- There are no repeated domain values.
3. A relation is a function if each domain value maps to exactly one unique range value. In this case, each domain value ([tex]\(-3, -1, 1, 5\)[/tex]) maps to a range value [tex]\((-2, 0, 0, -2) respectively). None of the domain values \( -3, -1, 1, 5\)[/tex] are repeated with different range values.
Since each domain value has a unique corresponding range value (though some range values like 0 and -2 are repeated, this doesn't affect whether it's a function), the relation satisfies the condition of being a function.
Thus, the answer is:
[tex]\[ \text{Yes; only one range value exists for each domain value.} \][/tex]
