Example
List the domain and range for the following table of values where
x is the input and
y is the output.
x |
y |
−3 |
4 |
−2 |
4 |
−1 |
4 |
2 |
4 |
3 |
4 |
Answer:
The domain describes all the inputs, and we can use set notation with brackets { } to make the list.
Domain:{−3,−2,−1,2,3}
The range describes all the outputs.
Range:{4}
We only listed 4 once because it is not necessary to list it every time it appears in the range.
In the following video we provide another example of identifying whether a table of values represents a function as well as determining the domain and range of each.
[embed]https://youtu.be/y2TqnP_6M1s[/embed]
Example
Define the domain and range for the following set of ordered pairs, and determine whether the relation given is a function.
{(−3,−6),(−2,−1),(1,0),(1,5),(2,0)}
Answer:
We list all of the input values as the domain. The input values are represented first in the ordered pair as a matter of convention.
Domain: {−3,−2,1,2}
Note how we did not enter repeated values more than once; it is not necessary.
The range is the list of outputs for the relation; they are entered second in the ordered pair.
Range: {−6,−1,0,5}
Organizing the ordered pairs in a table can help you tell whether this relation is a function. By definition, the inputs in a function have only one output.
x |
y |
−3 |
−6 |
−2 |
−1 |
1 |
0 |
1 |
5 |
2 |
0 |
The relation is not a function because the input
1 has two outputs:
0 and
5.
In the following video, we show how to determine whether a relation is a function and how to find the domain and range.
[embed]https://youtu.be/kzgLfwgxE8g[/embed]
Example
Find the domain and range of the relation and determine whether it is a function.
{(−3,4),(−2,4),(−1,4),(2,4),(3,4)}
Answer:
Domain: {−3,−2,−1,2,3}
Range: {4}
To help you determine whether this is a function, you could reorganize the information by creating a table.
x |
y |
−3 |
4 |
−2 |
4 |
−1 |
4 |
2 |
4 |
3 |
4 |
Each input has only one output, and the fact that it is the same output (4) does not matter.
This relation is a function.