Example

Determining the Domain, Graph, and Range of the Radical Function f(x)=x2f(x) = \sqrt{x - 2}

To analyze the radical function f(x)=x2f(x) = \sqrt{x - 2}, begin by establishing the domain. The index of the radical is even, which dictates that the radicand must be non-negative: x20x - 2 \ge 0. Therefore, the domain consists of all values where x2x \ge 2, written in interval notation as [2,)[2, \infty). To construct the graph, deliberately choose xx-values within this interval that will yield a perfect square radicand (like 22, 33, 66, and 1111) to calculate the matching yy-values (00, 11, 22, and 33). The resulting graph is a continuous curve that originates at (2,0)(2, 0). Observing this graph demonstrates that the yy-values are always greater than or equal to zero, which establishes that the range is [0,)[0, \infty).

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Updated 2026-05-25

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