1Cademy - Determining the Domain, Graph, and Range of the Radical Function $$f(x) = \sqrt{x

Learn Before

Example: Graphing the Function $f(x) = \sqrt{x}$

Example

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

To analyze the radical function $f(x) = \sqrt{x - 2}$ , begin by establishing the domain. The index of the radical is even, which dictates that the radicand must be non-negative: $x - 2 \ge 0$ . Therefore, the domain consists of all values where $x \ge 2$ , written in interval notation as [2, infty). To construct the graph, deliberately choose $x$ -values within this interval that will yield a perfect square radicand (like $2$ , $3$ , $6$ , and $11$ ) to calculate the matching $y$ -values ( $0$ , $1$ , $2$ , and $3$ ). The resulting graph is a continuous curve that originates at (2, 0). Observing this graph demonstrates that the $y$ -values are always greater than or equal to zero, which establishes that the range is [0, infty).

0

1

Updated 2026-06-03

Contributors are:

Who are from:

References

OpenStax Intermediate Algebra

Learn Before

Related

Learn After