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a function?
A relation is a function when each input has exactly one output.
How can you use different representations of a relation to determine whether the relation is a function?
Is a relation always a function? Is a function always a relation? Explain.
To determine whether a relation is a function, you can use different representations such as:
1. Ordered Pairs: Check if any input (first element) is associated with more than one output (second element). If an input has multiple outputs, it’s not a function.
2. Graphs: Use the vertical line test. If any vertical line intersects the graph at more than one point, the relation is not a function.
3. Tables: Look at the input values. If an input corresponds to more than one output value in the table, it’s not a function.
Now, regarding the relationship between functions and relations:
– A relation is not always a function because there can be inputs with multiple outputs.
– However, every function is a relation since it is a specific type of relation where each input has only one output.
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