Remember that a function is a type of relation in which there is exactly one output for each input.
Domain: {6,8,9,11} Range: {0,1,2,3} Interpretation of the Context: See solution. Relation: It is not a function.
Practice makes perfect
The following table represents the relation between the age of each student and the number of pets a student has.
Age
Number of Pets
6
3
8
2
9
0
11
1
11
2
We are asked to state domain and range, interpret the data in context, and explain if it is a function or not. We will accomplish these tasks one at a time.
Domain and Range
Let's determine the domain and the range of the relation. First, let's recall what the domain and range of a relation are.
The domain is the possible inputs of a relation.
The range is the possible outputs of a relation.
In this case, the age of each student will be the domain and the number of pets will be the range.
Domain:& {6,8,9,11}
Range:& {0,1,2,3}
Interpretation of the Context
Let's interpret the context depending on the inputs and outputs.
For an input of 6-year old student there is one output of 3 pets.
For an input of 8-year old student there is one output of 2 pets.
For an input of 9-year old student there is one output of 0 pets.
For an input of 11-year old student there are two outputs of 1 and 2 pets.
Is the relation a function?
A function is a type of relation for which there is exactly one output for each input. Therefore, our relation is not a function because there are two outputs (two different numbers of pets) for the input (age) of an 11-year old student.
