# Range

### From Conservapedia

In mathematics, the **range** (or **image**) of a function are the values it hits. It is not to be confused with the codomain of a function, which is a designated set to which all the values of the function belong.

A function is onto (or surjective) if every value in its codomain is hit by the function, or, equivalently, if its range is equal to its codomain. More formally, a function is onto if for every there exists such that
*f*(*x*) = *y*.

## Examples

Let be the function defined by the equation *f*(*x*) = *x*^{2}. By definition, the codomain
of *f* is . However, the range of *f* consists of all nonnegative real numbers. Indeed, let *y* be a nonnegative real number. Then , and so *y* is one of the values hit by *f*.

Let be the function defined by the equation *g*(*x*) = *x* + 1. Then, for every real number
*y*, we can see that *g*(*y* − 1) = (*y* − 1) + 1 = *y*, so every real number is hit by *g*. This means that the codomain and range of *g* are equal, namely . Therefore, *g* is onto.

## Non-mathematical uses

A range can also refer to a type of oven.