Which functions are mentioned in Objective C.

Figure, function - Serlo "Math for non-freaks"

Figure, function [edit]

A central concept in mathematics is that Illustrationthat too function is called. Illustrations are clear associations between two sets and . This means every item through the figure exactly one element is assigned. An example of this is the square function of the set in the crowd that are any real number their square number assigns. The notation for illustrations of to is:

This expression is pronounced like this:

The amount called Domain of definition of and is the Target amount the figure. The elements from the domain of become argument called and each element hit by the mapping called Function value to the argument .


The terms "mapping" and "function" are both common in mathematics and mean exactly the same thing.

In the target set not all elements have to be function values.

example (Remainder when dividing by 2)

Here is the domain of definition of four elements. The target amount is . and are function values. The number on the other hand not, because no number results in division by the rest . So not all elements are in Function values.

The arrows show the assignment: they go from the argument to the function value and thus connect a pair. We can therefore do the assignment describe as a set of pairs of argument and function value: . We already got to know sets of pairs in the chapter Relation. So images are relations! But not every relation is an illustration. For a relation to be a map, each element in in relation to exactly one element in be

Let's summarize again what defines a function: the couples form a relation . This relation has a special property: to each element there is exactly one element With . You can recognize this in the arrow diagram by the fact that of each element of the definition range exactly one arrow goes out. In the coordinate system it has to go to everyone -Value exactly one -Give value.

The quadratic function

We therefore define mappings as a relation with the property mentioned above:

example (Square function)

Every real number is assigned its square:

Functions are often illustrated in the coordinate system, as in the illustration of the function on the right. In doing so, the couples understood as coordinates. This point set is then called graph the function.

Understanding question: Which of the following arrow diagrams represent images from the crowd in the crowd dar?

Definition and value range [edit]

Is a function of to , so is the Domain of definition of

The Range of values a function is defined as the set of function values:

definition (Value range of a function)

be a function. Then that is Range of values of formalizes the set of all elements for which there is an argument: