To determine which two ordered pairs can be removed to leave a remaining set that is a function, we need to remember that a function cannot have two different ordered pairs that share the same first element (x-coordinate).
Let's analyze the given set of ordered pairs:
- (-3, 1)
- (5, 2)
- (2, -3)
- (3, 2)
- (-5, 1)
Now, let's look at the x-coordinates:
- -3 appears once
- 5 appears once
- 2 appears once
- 3 appears once
- -5 appears once
Since all x-coordinates are unique, we currently have a functioning set. Hence, for any combination of pairs removed from this set, we need to ensure that all remaining pairs still have unique x-coordinates.
Analysis of possible removals:
One strategy is to attempt removing pairs that share x-coordinates, but here, every pair has unique x-coordinates. Therefore, we can actually remove any two pairs without affecting the function property.
In conclusion, any two of the given ordered pairs can be removed, and the remaining set will still be a function. For example, if we remove (-3, 1) and (5, 2), the remaining pairs would be:
- (2, -3)
- (3, 2)
- (-5, 1)
These still adhere to the rule of a function, which implies that they would yield unique outputs based on unique inputs.
Answer:
Any two pairs can be removed; e.g., remove (-3, 1) and (5, 2). The remaining set will still be a function.
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