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Is the relation a function? {(3, 4), (5, 0), (2, 4), (-5, -5)}

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Final answer:

The relation given, consisting of the ordered pairs {(3, 4), (5, 0), (2, 4), (-5, -5)}, is a function because each input (x-coordinate) has a unique output (y-coordinate).

Step-by-step explanation:

Whether a relation is a function or not can be determined by looking at the set of ordered pairs. A relation is a function if for every input (x value) there is only one output (y value). In other words, in the set of ordered pairs, each x-coordinate must be unique for the relation to be considered a function.

The set of ordered pairs given is {(3, 4), (5, 0), (2, 4), (-5, -5)}. Here, we can see that all the x-coordinates are unique: 3, 5, 2, and -5. Since no x value repeats, it implies that each input corresponds to exactly one output, which satisfies the definition of a function. Therefore, this relation is a function.

Remember, when looking for a dependence of y on x, we are seeking to ensure that for each x there is one and only one possible y, which is at the heart of the definition of a function in mathematics.

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