Let's have a look...
If you have two sets of values, the connection between the values is called a relation. Some relations are functions because each value in the first set is related to one, and only one, value in the second set.
You may have noticed that the values are presented in a particular order for both relations and functions. You may even have noticed in the mapping diagrams that the arrow heads pointed in a single direction. This is because the values in one set were considered the input and the values in the other set were the output.
This mapping diagram represents a function. The blue set contains the input values, and the yellow set contains the output values. You know this because the arrowheads point to the output values.
Reminder
The set of input values are also called the domain, and the set of output values are the range. In an ordered pair or on a coordinate graph, the x-values represent the domain, and the y-values represent the range.
You can name the domain and range of both relations and functions.
Give the domain and the range for Ms. Kendall’s table, where the input value is the amount of time studied and the quiz score earned is the output value.
| Student | Amount of Time Studied (minutes) | Quiz Score Earned (percentage) |
|---|---|---|
| 1 | 30 | 84 |
| 2 | 10 | 52 |
| 3 | 15 | 66 |
| 4 | 20 | 84 |
| 5 | 20 | 61 |
| 6 | 60 | 100 |
| 7 | 25 | 94 |
| 8 | 15 | 80 |
| 9 | 0 | 72 |
| 10 | 35 | 90 |
| The domain consists of all the input values. Duplicate values are listed only once. The curly braces indicate that these values are the set that makes up the domain. |
{0, 10, 15, 20, 25, 30, 35, 60} Generally, the values are listed from smallest to largest. |
| The range is all the output values. Duplicate values are listed only once. The curly braces indicate that these values are the set that makes up the range. |
{52, 61, 66, 72, 80, 84, 90, 87, 100} Generally, the values are listed from smallest to largest. |
Give it a shot!
How well can you use tables, ordered pairs, graphs, and mapping diagrams to identify the domain and range of relations and functions? Use the activity below to practice. View the display on each tab and name the domain and range of the relation or function. Then check your answer.
The domain is {0, 1, 2, 3}
The range is {0, 1.69, 3.38, 5.07}
If you need help arriving at this answer, click the solution button.
| The domain consists of all the input values. | The blue set represents the domain. The values are {0, 1, 2, 3}. |
| The range is all the output values. | The yellow set represents the range. The values are {0, 1.69, 3.38, 5.07}. |
Set 1 represents the input values.
| Set 1 | Set 2 |
| -1 | 5 |
| 0 | 3 |
| 1 | 5 |
| 2 | 11 |
The domain is {–1, 0, 1, 2}.
The range is {3, 5, 11}.
If you need help arriving at this answer, click the solution button.
| The domain consists of all the input values. | The values are {–1, 0, 1, 2}. |
| The range is all the output values. Remember that duplicate values are listed only once. |
The values are {3, 5, 11}. |
{(7, 9), (8, 10), (9, 11), (8, 12)}
The domain is {7, 8, 9}.
The range is {9, 10, 11, 12}.
If you need help arriving at this answer, click the solution button.
| The domain consists of all the input values. Remember that duplicate values are listed only once. |
The values are {7, 8, 9}. |
| The range is all the output values. | The values are {9, 10, 11, 12}. |
The domain is {–60, 20, 70}.
The range is {–6, 2, 3, 5}.
If you need help arriving at this answer, click the solution button.
| The domain consists of all the input values. | The values are {–60, 20, 70}. |
| The range is all the output values. | The values are {–6, 2, 3, 5}. |
The domain is {–2, 0, 1, 3}.
The range is {15, 20, 30, 40}.
If you need help arriving at this answer, click the solution button.
| The domain consists of all the input values. | The values are {–2, 0, 1, 3}. |
| The range is all the output values. | The values are {15, 20, 30, 40}. |
