What is the range of the function y=√x ?

For any function, the range is the complete set of output values (y-values) it can produce; it depends on both the domain (permitted inputs) and the function's own value restrictions, not on inspecting the formula alone. For the square root function y=√x, the radicand must be non-negative for a real output, so x≥0 is required, and the principal square root itself is defined to be non-negative (√x≥0 for every valid x).

1. Domain: a real output requires x≥0.

2. Since the principal square root is always ≥0, the smallest possible output occurs at x=0, giving y=√0=0.

3. As x increases without bound, √x also increases without bound, so y can take any value from 0 upward.

4. So the range is [0,∞): 0 is included because it is attained at x=0, and there is no upper bound.

Sample inputs confirm this: x=0 → y=0 (the boundary point is attained), x=1 → y=1, x=4 → y=2, x=9 → y=3 — every output is ≥0 and grows without limit, matching [0,∞) exactly and ruling out any interval that excludes 0 or admits negative values.