# Definition:Real Function/Range

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*This page is about Range of Real Function. For other uses, see Range.*

## Definition

Let $S \subseteq \R$.

Let $f: S \to \R$ be a real function.

The range of $f$ is the set of values that the dependent variable can take.

That is, it is the image set of $f$.

## Also known as

Modern treatments of the subject are usually more precise.

In particular, the word **range** may be taken to mean codomain.

## Sources

- 1963: Morris Tenenbaum and Harry Pollard:
*Ordinary Differential Equations*... (previous) ... (next): Chapter $1$: Basic Concepts: Lesson $2 \text B$: The Meaning of the Term*Function of One Independent Variable*