y = sin(x)
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The domain of the sine function is all real numbers.
The domain can be anything you like, from the whole of the real numbers to just a single value.
The domain is whatever you want it to be. In the absence of a domain being defined explicitly, it is taken to be the whole of the real line.
False
The function is a simple linear function and so its nature does not limit the domain or range in any way. So the domain and range can be the whole of the real numbers. If the domain is a proper subset of that then the range must be defined accordingly. Similarly, if the range is known then the appropriate domain needs to be defined.