### 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.

Consider the following:

$\text{A relation is a function when there is only one output for each input.}$

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.

$\boxed{\text{Function}}$