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Answer :
Final answer:
The function f(x) = 35x⁵ has a domain and range of all real numbers, making the correct answer option a) Domain: (-∞, ∞), Range: (-∞, ∞).
Explanation:
The function given is f(x) = 35x⁵, which is a polynomial of degree five. The domain of a polynomial is the set of all real numbers because there is no restriction on the values that x can take in a polynomial expression. Therefore, the domain of this function is (-∞, ∞). As for the range, since it is an odd-degree polynomial, as x approaches infinity, f(x) approaches infinity, and as x approaches negative infinity, f(x) approaches negative infinity. Hence, the range of this function is also (-∞, ∞). Therefore, the correct answer is option a): Domain: (-∞, ∞), Range: (-∞, ∞).
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