# Names of function

For any function that converts/computes some integer into another integer or be it a real number to another real number. What is the correct teminology to use for this kind of function? I can't think of it as being a mapping function, seems that wikipedia describes mapping function as something else involving more complex topics. Im no map wiz.

For example $f(x) = 2x$, where $x \in \mathbb{N}_+$ or $\mathbb{Z}_+$ (for any positive integer in the input domain) the function transforms $x$ into one number in the range of even positive integers.

How can I refer to this function? Transform function? Mapping function? Does it have a special name? Say I have several functions that use $f(x)$ later on. $g(x) = f(x)+h(x)$ etc.. does $g(x)$ have a special name other than $f(x)$ or... I would like some simple answer on this.

Thanks

• It's not clear how what you are describing is different from any other kind of function. I would say the word you are looking for is just "function". – Eric Wofsey Jun 8 '18 at 22:56
• If I understood you: $f:D\to C$ where $D$ is the domain and $C$ the codomain. If $f(x)=x$ then $f:\Bbb R\to\Bbb R$ means it takes real numbers, but $f:\Bbb N\to \Bbb R$ means it takes only natural numbers as input.(But all of those are still called just function) – Holo Jun 8 '18 at 22:57
• I would add that a function that takes in values from the positive integers is also called a sequence. – giobrach Jun 8 '18 at 22:59
• @Eric Wofsey: Ok, I guess you're right. – Natural Number Guy Jun 8 '18 at 23:13
• @NaturalNumberGuy in the definition of function the codomain is a set contains the possible outputs, but may contain more elements, if it does not contain other elements we say the function is "onto" or "surjective"(I usually don't use range because range is sometimes used as codomain and sometimes as the image: here is more of why) – Holo Jun 8 '18 at 23:53

the notation $f:A\to B$ where $f$ is the name of the function, $A$ is the domain and $B$ is the range, explains everything.