Question

A set of ordered pairs is shown in the table.



Removing which two of the following ordered pairs from the table would leave a remaining set that is a function?

(-3, 1)
(5, 2)
(2, -3)
(3, 2)
(-5, 1)

Answer 1

To determine which two ordered pairs to remove to leave a remaining set that is a function, we need to remember that a function cannot have two ordered pairs with the same first element (x-coordinate).

Let’s analyze the x-coordinates of the given ordered pairs:

1. (-3, 1) → x = -3
2. (5, 2) → x = 5
3. (2, -3) → x = 2
4. (3, 2) → x = 3
5. (-5, 1) → x = -5

All x-coordinates are distinct (-3, 5, 2, 3, -5). This means that there are no duplicates, and thus, the set of ordered pairs is already a function.

Since there is no immediate need to remove any pairs for the set to qualify as a function, if we want to select any two pairs for removal, we can choose any two pairs.

For example, we could remove:

1. (-3, 1)
2. (5, 2)

This would still leave the ordered pairs (2, -3), (3, 2), and (-5, 1) which is a function since none of these ordered pairs share the same first coordinate.

In conclusion, you can remove any two pairs and the remaining set will still be a function.