To find the domain or range, solve for a variable and see if the other variable has any restrictions on it. In this case, x2 + y = 4
y = 4 - x2
There are no restrictions on x, therefore x is in the domain of all real numbers.
x = square root(4 - y)
Since the argument (number in brackets) of a square root must be positive, 4 - y > 0, y < 4.
Domain: x can be all real numbers.
Range: y can be all real numbers less than or equal to 4.
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The range is {-7, 1, 9, 17}.
You can define the domain as anything you like and that will determine the range. Or, you can define the range as anything you like and that will determine the domain. For example: domain = {1, 2, 3, 4, ... } then range = {-3, 0, 5, 12, ... } or range = {1, 2, 3, 4, ... } then domain = {sqrt(5), sqrt(6), sqrt(7), sqrt(8), ...}. There is, of course, no need to restrict either set to integers but then it was easier to work out one set from the other.
The domain is the whole real line (or complex plane).
the domain is all real numbers and the range is all real numbers the domain is all real numbers and the range is all real numbers
The range could be anything. Without parameters specified, the domain of {1,2,3,4} could have any range. This problem is unsolvable.