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From Conservapedia - Reading time: 1 min

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 $\text{[math]}$ is onto if for every $\text{[math]}$ there exists $\text{[math]}$ such that $\text{[math]}$ .

Examples[edit]

Let $\text{[math]}$ be the function defined by the equation $\text{[math]}$ . By definition, the codomain of $\text{[math]}$ is $\text{[math]}$ . However, the range of $\text{[math]}$ consists of all nonnegative real numbers. Indeed, let $\text{[math]}$ be a nonnegative real number. Then $\text{[math]}$ , and so $\text{[math]}$ is one of the values hit by $\text{[math]}$ .

Let $\text{[math]}$ be the function defined by the equation $\text{[math]}$ . Then, for every real number $\text{[math]}$ , we can see that $\text{[math]}$ , so every real number is hit by $\text{[math]}$ . This means that the codomain and range of $\text{[math]}$ are equal, namely $\text{[math]}$ . Therefore, $\text{[math]}$ 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

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