Difference between revisions of "Range"
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==Non-mathematical uses== | ==Non-mathematical uses== | ||
| + | * A range can also refer to a type of oven. | ||
| + | * [[Shooting range]] | ||
| + | * Range - see [[distance]] and [[rangefinder]] in target and [[sniper]] [[shooting]] | ||
| − | + | [[Category : Mathematics]] | |
| − | + | [[Category : Firearms Glossary]] | |
| − | [[Category: | + | [[Category : Firearms]] |
Revision as of 09:30, March 6, 2015
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
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
- A range can also refer to a type of oven.
- Shooting range
- Range - see distance and rangefinder in target and sniper shooting
