Subjects algebra

Domain Range F80A85

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1. The problem asks to identify the domain and range of the given relation: $\{(3, -2), (0, 7), (2, -1), (4, 3)\}$.\n\n2. The domain of a relation is the set of all first elements (x-values) in the ordered pairs.\n\n3. The range of a relation is the set of all second elements (y-values) in the ordered pairs.\n\n4. Extract the domain from the relation: $\{3, 0, 2, 4\}$.\n\n5. Extract the range from the relation: $\{-2, 7, -1, 3\}$.\n\n6. Now, compare the range set $\{-2, 7, -1, 3\}$ with the given options:\n- A. $\{\text{all real numbers}\}$ - Incorrect, range is limited to specific values.\n- B. $\{0, 1, 2, 3, 4\}$ - Incorrect, does not match the range values.\n- C. $\{0, 2, 3, 4\}$ - Incorrect, does not match the range values.\n- D. $\{-1, -2, 3, 7\}$ - Correct, matches the range exactly.\n\nFinal answer: The domain is $\{0, 2, 3, 4\}$ and the range is $\{-1, -2, 3, 7\}$, so the correct range option is D.