### Identifying Functions from Relations In this activity, we explore how to determine if a given relation is a function. A relation is a set of ordered pairs, and a function is a specific type of relation where each input (or domain value) is associated with exactly one output (or range value). #### Relation 1 | Domain | Range | |--------|-------| | r | z | | u | s | | z | s | | y | s | | b | s | - **Analysis**: Each domain value corresponds to exactly one range value. - **Conclusion**: This relation *is* a function. #### Relation 2 | Domain | Range | |--------|-------| | 0 | pen | | -9 | tree | | -9 | sky | | 4 | pen | | 8 | sky | - **Analysis**: The domain value -9 corresponds to two different range values (tree and sky). - **Conclusion**: This relation is *not* a function. #### Relation 3 {(0, 4), (4, 6), (6, 6), (9, 4)} - **Analysis**: Each domain value is paired with only one range value. - **Conclusion**: This relation *is* a function. #### Relation 4 {(d, -4), (f, -4), (j, -4), (a, -4)} - **Analysis**: Each domain value corresponds to exactly one range value, though all range values are the same. - **Conclusion**: This relation *is* a function. #### Summary To identify a function, ensure no domain value maps to multiple range values. This key property distinguishes functions from general relations. Use this guideline to analyze the provided relations effectively.
### Identifying Functions from Relations In this activity, we explore how to determine if a given relation is a function. A relation is a set of ordered pairs, and a function is a specific type of relation where each input (or domain value) is associated with exactly one output (or range value). #### Relation 1 | Domain | Range | |--------|-------| | r | z | | u | s | | z | s | | y | s | | b | s | - **Analysis**: Each domain value corresponds to exactly one range value. - **Conclusion**: This relation *is* a function. #### Relation 2 | Domain | Range | |--------|-------| | 0 | pen | | -9 | tree | | -9 | sky | | 4 | pen | | 8 | sky | - **Analysis**: The domain value -9 corresponds to two different range values (tree and sky). - **Conclusion**: This relation is *not* a function. #### Relation 3 {(0, 4), (4, 6), (6, 6), (9, 4)} - **Analysis**: Each domain value is paired with only one range value. - **Conclusion**: This relation *is* a function. #### Relation 4 {(d, -4), (f, -4), (j, -4), (a, -4)} - **Analysis**: Each domain value corresponds to exactly one range value, though all range values are the same. - **Conclusion**: This relation *is* a function. #### Summary To identify a function, ensure no domain value maps to multiple range values. This key property distinguishes functions from general relations. Use this guideline to analyze the provided relations effectively.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Transcribed Image Text:### Identifying Functions from Relations
In this activity, we explore how to determine if a given relation is a function. A relation is a set of ordered pairs, and a function is a specific type of relation where each input (or domain value) is associated with exactly one output (or range value).
#### Relation 1
| Domain | Range |
|--------|-------|
| r | z |
| u | s |
| z | s |
| y | s |
| b | s |
- **Analysis**: Each domain value corresponds to exactly one range value.
- **Conclusion**: This relation *is* a function.
#### Relation 2
| Domain | Range |
|--------|-------|
| 0 | pen |
| -9 | tree |
| -9 | sky |
| 4 | pen |
| 8 | sky |
- **Analysis**: The domain value -9 corresponds to two different range values (tree and sky).
- **Conclusion**: This relation is *not* a function.
#### Relation 3
{(0, 4), (4, 6), (6, 6), (9, 4)}
- **Analysis**: Each domain value is paired with only one range value.
- **Conclusion**: This relation *is* a function.
#### Relation 4
{(d, -4), (f, -4), (j, -4), (a, -4)}
- **Analysis**: Each domain value corresponds to exactly one range value, though all range values are the same.
- **Conclusion**: This relation *is* a function.
#### Summary
To identify a function, ensure no domain value maps to multiple range values. This key property distinguishes functions from general relations. Use this guideline to analyze the provided relations effectively.
Expert Solution
Step 1
Consider the following:
And each value of x should be related to any value of y.
Consider the relation 1:
This is a function since there is only one output for each input. And every input has its output.
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Solved in 2 steps
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