3-2 Relations and Functions
Lesson Objective: Identify functions and find the domain and the range of both relations and functions.
Vocabulary Words: Relation,Domain, Range,and Function
Relations and functions can be used in real life situations such as: the scoring system of a track meet.
Ordered pairs that represent relationships are called relations.
The domain of a relation is the set of first coordinates of the ordered pairs(x-values).
The range of a relation is the set of second coordinates of the ordered pairs (y-values).
A function is a special type of relation that pairs each domain value with only one range value.
There are multiple representations of functions, here are a few examples of them:
This is the mapping diagram form of a function.
As you can see, not all the y-values have been paired with an x-value, which isn’t required to make a mapping diagram form of a function.
However, it is required to have each domain value paired with only one range value. Mapping diagrams are used to determine whether a group of ordered pairs is a function or not.
This is the graph form of a function.
To make a graph function, all you have to do is plot the ordered pairs in points on the graph.
This is the table form of a function.
All you have to do to make one is to organize the domain and range into two groups, in the form of a table. The domains of a relation are all the x-values of the ordered pairs, and the ranges of a relation are all the y-values of the ordered pairs. To identify between a function and a relation, you must use a mapping diagram. If one or more x-values are paired up with more than one y-value, the ordered pairs are not a function.