1Cademy - Determining the Domain, Graph, and Range of the Radical Function $$f(x) = \sqrt{x + 2}$$

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

Example

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

For the radical function $f(x) = \sqrt{x + 2}$ , the first step is to find the domain. Because the radical has an even index ( $2$ ), the radicand must be greater than or equal to zero ( $x + 2 \ge 0$ ). Solving this indicates that $x \ge -2$ , so the domain is $[-2, \infty)$ in interval notation. To graph the function, select $x$ -values in this domain that produce perfect squares under the radical—such as $-2$ , $-1$ , $2$ , and $7$ —to easily evaluate the corresponding $y$ -values ( $0$ , $1$ , $2$ , and $3$ ). By plotting these ordered pairs and connecting them, the graph visually confirms that the $y$ -values are strictly greater than or equal to zero. Consequently, the range of the function is $[0, \infty)$ .

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Updated 2026-05-26

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OpenStax Intermediate Algebra

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