Example
List the domain and range for the following table of values where
x is the input and
y is the output.
x |
y |
[latex]−3[/latex] |
[latex]4[/latex] |
[latex]−2[/latex] |
[latex]4[/latex] |
[latex]−1[/latex] |
[latex]4[/latex] |
[latex]2[/latex] |
[latex]4[/latex] |
[latex]3[/latex] |
[latex]4[/latex] |
Answer:
The domain describes all the inputs, and we can use set notation with brackets { } to make the list.
[latex-display]\text{Domain}:\{-3,-2,-1,2,3\}[/latex-display]
The range describes all the outputs.
[latex-display]\text{Range}:\{4\}[/latex-display]
We only listed [latex]4[/latex] once because it is not necessary to list it every time it appears in the range.
Watch the following video for another example of how to identify whether a table of values represents a function and how to determine the domain and range.
[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.
[latex]\{(−3,−6),(−2,−1),(1,0),(1,5),(2,0)\}[/latex]
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: {[latex]-3,-2,1,2[/latex]}
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: {[latex]-6, -1, 0, 5[/latex]}
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 |
[latex]−3[/latex] |
[latex]−6[/latex] |
[latex]−2[/latex] |
[latex]−1[/latex] |
[latex]1[/latex] |
[latex]0[/latex] |
[latex]1[/latex] |
[latex]5[/latex] |
[latex]2[/latex] |
[latex]0[/latex] |
The relation is not a function because the input [latex]1[/latex] has two outputs: [latex]0[/latex] and [latex]5[/latex].
The following video shows how to determine whether a relation given in non-tabular form 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.
[latex]\{(−3, 4),(−2, 4),( −1, 4),(2, 4),(3, 4)\}[/latex]
Answer:
Domain: {[latex]-3, -2, -1, 2, 3[/latex]}
Range: {[latex]4[/latex]}
To help you determine whether this is a function, you could reorganize the information by creating a table.
x |
y |
[latex]−3[/latex] |
[latex]4[/latex] |
[latex]−2[/latex] |
[latex]4[/latex] |
[latex]−1[/latex] |
[latex]4[/latex] |
[latex]2[/latex] |
[latex]4[/latex] |
[latex]3[/latex] |
[latex]4[/latex] |
Each input has only one output, and the fact that it is the same output (4) does not matter.
This relation is a function.