Range

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 .

## Examples[edit]

Let  be the function defined by the equation . By definition, the codomain of  is . However, the range of  consists of all nonnegative real numbers. Indeed, let  be a nonnegative real number. Then , and so  is one of the values hit by .

Let  be the function defined by the equation . Then, for every real number , we can see that , so every real number is hit by . This means that the codomain and range of  are equal, namely . Therefore,  is onto.

## Non-mathematical uses[edit]

* A range can also refer to a type of oven.
* Shooting range
* Range - see distance and rangefinder in target and sniper shooting