Final answer:
The domain of the function y = 4sin(x) is all real numbers, as the sine function is defined for any real number, resulting in a domain of (-∞, ∞).
Step-by-step explanation:
The domain of a function refers to the set of all possible input values (usually x-values) for which the function is defined. In the case of the function y = 4sin(x), the sine function can accept any real number as its input, since the sine function is defined for all real numbers. This means that the domain of this function is all real numbers, symbolically written as (-∞, ∞).
The function given in the question, y = 4sin(x), is consistent with sine's properties because the sine function oscillates between +1 and -1, and as such, any real number input will yield a valid output between -4 and 4 after being multiplied by 4, reflecting the sine's amplitude modulation in the function.