Is Relation 2 a function or not a function?
| Domain | Range |
|---|---|
| 6 | cloud |
| -5 | sky |
| 9 | tree |
| -1 | tree |
| -5 | cloud |
Answer (2)
A relation is a function if each domain value maps to a unique range value. The domain value -5 maps to both 'sky' and 'cloud'. Therefore, the given relation is not a function.
Explanation
Understanding Functions A function is a relation where each input (domain value) corresponds to exactly one output (range value). In other words, for every value in the domain, there can only be one corresponding value in the range.
Analyzing the Relation We are given a relation in a table format. The table shows the mapping between domain and range values. We need to check if any domain value maps to more than one range value.
Identifying Non-Functionality Looking at the table, we see that the domain value 6 maps to 'cloud', -5 maps to 'sky', 9 maps to 'tree', -1 maps to 'tree', and -5 maps to 'cloud'. The domain value -5 appears twice, mapping to 'sky' and 'cloud'. Since one domain value (-5) maps to two different range values ('sky' and 'cloud'), the relation is not a function.
Conclusion Therefore, the given relation is not a function.
Examples
In everyday life, functions are used to describe relationships between different quantities. For example, the price of an item is a function of its quantity. If you buy one apple, it costs a certain amount; if you buy two, it costs twice as much (assuming a constant price per apple). Similarly, the distance traveled by a car is a function of time, given a constant speed. Understanding functions helps us model and predict these relationships.
The given relation is not a function because the domain value -5 maps to two different range values: 'sky' and 'cloud'. According to the definition of a function, each domain value must correspond to exactly one range value. Therefore, this relation does not satisfy the criteria of a function.
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