Domain and Range of Square and Cube Root Functions
You can also find the domain and range of square root and cube root functions. When working with square root functions, it is important to remember that the radicand must be greater than or equal to zero. If it is less than zero then we are working with imaginary numbers. Let's look at an example of finding the domain of a square root function.
To find the domain you know that 2x + 4 must be greater than or equal to zero. The next step is to solve for x.
2x + 4 ≥ 0
2x ≥ -4
x ≥ -2
The domain of the function is x ≥ -2.
If we look at the same function 
but want to find the range, we need to find all the possible values of f(x) or y. Notice that this function has no vertical shift and therefore the range is
y ≥ 0.
If we changed the function to 
there is a vertical shift of 3 units down. The range of this function is y ≥ -3.
If you analyze the graph of 
and any transformations of this parent function, you will notice that both the domain and range are always All Real Numbers. Any radical function with an index that is a positive odd integer will have a domain and range that are All Real Numbers.
