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In mathematical analysis, and applications in geometry, applied mathematics, engineering, and natural sciences, a function of a real variable is a function whose domain is the real numbers ℝ, or a subset of ℝ that contains an interval of positive length. Most real functions that are considered and studied are differentiable in some interval.
The most widely considered such functions are the real functions, which are the real-valued functions of a real variable, that is, the functions of a real variable whose codomain is the set of real numbers.

### Real function

### General definition

### Calculus

### Implicit functions

### One-dimensional space curves in ℝ<sup>''n''</sup>

### Matrix valued functions

### Banach and Hilbert spaces and quantum mechanics

### Cardinality of sets of functions of a real variable