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.
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.
The answer depends on the domain. If the domain is the whole of the real numbers, the range in y ≥ 1. However, you can choose to have the domain as [1, 2] in which case the range will be [2, 5]. If you choose another domain you will get another range.
The domain is from negative infinity to positive infinity. The range is from positive 2 to positive infinity.
The domain would be (...-2,-1,0,1,2...); the range: (12)
The range is {-5, -2, 1, 4}
(x^2)^(1/2) equals x, therefore, y = x+4, which has a range and domain of all real numbers. The graph is a straight line, slope of 1, y-intercept of 4. Are you actually saying y = (x^2+4)^(1/2). If so, the range and domain will also be all real numbers because x^2+4 will never result in a negative number.
The domain is (-infinity, infinity) The range is (-3, infinity) and the asymptote is y = -3
The domain and the range depends on the context. For example, the domain and the range can be the whole of the complex field. Or I could define the domain as {-2, 1, 5} and then the range would be {0, 3, -21}. When either one of the range and domain is defined, the other is implied.
D=All reals R=All reals
f(x)=2x+2. Put in 0, 1/2, 1, 3/2, 2... and you will get integer values. That is for the domain. The numbers you get when you put that in are the range integral values.
The simplest answer is that the domain is all non-negative real numbers and the range is the same. However, it is possible to define the domain as all real numbers and the range as the complex numbers. Or both of them as the set of complex numbers. Or the domain as perfect squares and the range as non-negative perfect cubes. Or domain = {4, pi} and range = {8, pi3/2} Essentially, you can define the domain as you like and the definition of the range will follow or, conversely, define the range and the domain definition will follow,
This is the graph of a diagnol line. Range: (-infinity, infinity)
The domain could be the real numbers, in which case, the range would be the non-negative real numbers.