Introduction to Function rule definition:
Let us consider a set of items which are described in an ordered manner. The set expresses a relation between the items. This is general conclusion. If the relation is refined and could convey something better, then the relation becomes a function.
Let us discuss in detail with a simple example function rule definition.
Function Rule Definition – Basic Concept
Imagine a situation of a class teacher taking down the details of the ages of all the students. The teacher enters the record in an ordered manner, first the name of the student and his or her age next. The completed record now becomes a data set.
The items that come first in the set is called the domain set of the complete set. The items that come next is called the range set.
In this particular data set there is no condition exists between the items of the domain set and the items in the range set excepting that the information is ordered. Hence this data set expresses just a relation.
Consider another situation. A data is collected for miles into kilometer conversion. The domain set contains items like 1mi, 2 mi, 3mi …….. and the range set consists of the equivalent measure in kilometers as 1.6 km, 3.2 km, 4.8 km….. In this set the relation between the items in both the sets is refined. That is, the items are related by a function.
Function Rule Definition – the Rule
Definition of function rule:Consider a set of domain elements and the corresponding range elements.
If an item of the domain set corresponds to only and exactly one element in the range set, then the relation is a function.
Even if more than one element in the domain set correspond to one element in the range set, still the relation is a function. For example more than one student can be of the same age.
If an item in the domain set correspond to more than a single item in the range set, the relation is not a function. For example, a student corresponds different ages is meaningless.
Let us consider a set of items which are described in an ordered manner. The set expresses a relation between the items. This is general conclusion. If the relation is refined and could convey something better, then the relation becomes a function.
Let us discuss in detail with a simple example function rule definition.
Function Rule Definition – Basic Concept
Imagine a situation of a class teacher taking down the details of the ages of all the students. The teacher enters the record in an ordered manner, first the name of the student and his or her age next. The completed record now becomes a data set.
The items that come first in the set is called the domain set of the complete set. The items that come next is called the range set.
In this particular data set there is no condition exists between the items of the domain set and the items in the range set excepting that the information is ordered. Hence this data set expresses just a relation.
Consider another situation. A data is collected for miles into kilometer conversion. The domain set contains items like 1mi, 2 mi, 3mi …….. and the range set consists of the equivalent measure in kilometers as 1.6 km, 3.2 km, 4.8 km….. In this set the relation between the items in both the sets is refined. That is, the items are related by a function.
Function Rule Definition – the Rule
Definition of function rule:Consider a set of domain elements and the corresponding range elements.
If an item of the domain set corresponds to only and exactly one element in the range set, then the relation is a function.
Even if more than one element in the domain set correspond to one element in the range set, still the relation is a function. For example more than one student can be of the same age.
If an item in the domain set correspond to more than a single item in the range set, the relation is not a function. For example, a student corresponds different ages is meaningless.
