To determine which ordered pair can be removed to make the relation a function, we need to understand the definition of a function. A relation is a function if every input (or first element of the ordered pair) has exactly one corresponding output (or second element).
Now, let's examine the ordered pairs in the given relation:
- (0, 0)
- (2, 0.5)
- (4, 1)
- (3, 1.5)
- (4, 2)
- (5, 1.5)
- (6, 8)
From this list, we see that the input "4" appears twice:
- (4, 1)
- (4, 2)
Since the input "4" has two different outputs (1 and 2), this violates the definition of a function.
To make this relation a function, we can remove either (4, 1) or (4, 2).
Removing (4, 1): The resulting relation would be: {(0, 0), (2, 0.5), (4, 2), (3, 1.5), (5, 1.5), (6, 8)}
Removing (4, 2): The resulting relation would be: {(0, 0), (2, 0.5), (4, 1), (3, 1.5), (5, 1.5), (6, 8)}
In either case, the input "4" would only be associated with one output, which satisfies the condition for being a function.
Conclusion: Removing either (4, 1) or (4, 2) will make the relation a function because it ensures that each input has only one corresponding output.
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