The domain and range

Domain describes what the X part of a function is allowed to be - in other words where the line of the graph can go in terms of left and right. The parent radical function is f(x) = √(x). Because you cannot have a negative number under a square root sign, X has to be zero or positive. This means that the domain is greater than,or equal to, zero. The graph cannot go left of the Y-axis. Depending on which notation your teacher is having you use, it might look like this {X:X≥0} or [0,∞). The first one is in set builder notation, and the second one is in interval notation. The range describes what values the Y, or f(x), is allowed to have, or where the graph can go in terms of up/down. Because Y=√x, and the square root of a number is always positive, Y also has to be zero or positive. So, the range of the parent radical function is the same as the domain - {Y:Y≥0} or [0,∞). The graph cannot go below the X-axis.