domain is set of real numbers
range is set of real numbers
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The domain is what you choose it to be. You could, for example, choose the domain to be [3, 6.5] If the domain is the real numbers, the range is [-12.25, ∞).
The domain could be the real numbers, in which case, the range would be the non-negative real numbers.
x = the domain y = the co-domain and range is the output or something e_e
The domain is any subset of the real numbers that you choose, The range is the set of all values that the points in the domain are mapped to.
Find the range of a function by substituting the highest domain possible and the lowest domain possible into the function. There, you will find the highest and lowest range. Then, you should check all the possible cases in the function where a number could be divided by 0 or a negative number could be square rooted. Remove these numbers from the range. A good way to check to see if you have the correct range is to graph the function (within the domain, of course).