How can you use different representations of a relation to determine whether the relation is a function?

To determine whether a relation is a function, you can use different representations, such as:

1. Ordered Pairs: Check if any two ordered pairs have the same first element (input). If they do, the relation is not a function.

2. Graph: Look at the graph for the vertical line test. If a vertical line intersects the graph at more than one point, then the relation is not a function.

3. Table of Values: Examine the inputs and their corresponding outputs. If any input maps to more than one output, the relation is not a function.

Now, to address your second question:

– A relation is not always a function because a function requires each input to have a single, unique output, while a relation can have multiple outputs for a single input.

– A function is always a relation because a function is a specific type of relation that represents a special condition where each input maps to exactly one output.

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