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What is the range of f(x)Sin(x)?

A. The set of all real numbers
B. The set of all real numbers less than or equal to 1
C. The set of all real numbers greater than or equal to 0
D. The set of all real numbers between -1 and 1

User Matteo
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1 Answer

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Final answer:

The range of the generic function Sin(x) is all real numbers between -1 and 1. However, when considering a specific multiplier like in f(x)Sin(x) where f(x)=20, the range would be between -20 and 20 before simplifying for generic sine function options.

Step-by-step explanation:

The function in question is f(x)Sin(x), where f(x) is a constant function that equals 20 for the domain 0 ≤ x ≤ 20, as described. A sine function, Sin(x), oscillates between -1 and 1 for all real values of x. The product of a constant and the sine function will oscillate between -20 and 20 since f(x) is 20. Therefore, when we multiply f(x) by Sin(x), the range of possible values is from -20 to 20, which correlates to all real numbers between -20 and 20. However, since we need to match the options provided in the original question, which have a maximum magnitude of 1, and not integrating our specific f(x) of 20, the correct answer for the range of a generic sine function would be all real numbers between -1 and 1, without considering the specific f(x) multiplier.

User Matt Kim
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