Question

A set of ordered pairs is shown in the graph below.



Which two of the following ordered pairs could be added to the graph so that the set remains a function?

(-6, 0)
(-2, 3)
(-1, 8)
(3, -2)
(10, 6)

Answer 1

To determine which ordered pairs could be added to the graph while keeping the set a function, we need to remember the definition of a function: for every input (the first element of each ordered pair), there must be exactly one output (the second element).

This means that we should check whether the x-coordinates (the first elements of the ordered pairs) of the new pairs already exist in the set of ordered pairs in the graph. If an x-coordinate already exists, we cannot add the new pair without violating the definition of a function, unless its corresponding output matches the existing output.

Without seeing the specific graph or the existing ordered pairs, we need to make a general decision based on the x-coordinates of the pairs you provided:

1. **(-6, 0)**: Add if -6 doesn't already exist.
2. **(-2, 3)**: Add if -2 doesn't already exist.
3. **(-1, 8)**: Add if -1 doesn't already exist.
4. **(3, -2)**: Add if 3 doesn't already exist.
5. **(10, 6)**: Add if 10 doesn't already exist.

To find two pairs that can definitely be added, confirm that their x-values are not present in the existing set of ordered pairs.

If specific pairs from the graph are given, take note of their x-values to ensure you're selecting pairs with new x-values not present in those.

For instance, if the existing pairs had x-values of -6, -2, and 3, then (-1, 8) and (10, 6) can be added since they have unique x-values.

Please replace the checks according to the existing pairs in your graph to decide which two ordered pairs can be selected.