To determine which ordered pairs can be added to the existing set without violating the definition of a function, it's important to remember that each input (x-value) in the function must correspond to exactly one output (y-value). This means that no two ordered pairs can have the same x-value, even if they have different y-values.
To answer your question, you should check the x-values of the existing ordered pairs in the graph you mentioned, as well as the x-values of the provided options. For the ordered pairs to be valid additions while keeping the set a function, their x-values must not already be present in the graph.
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Extract x-values from the existing ordered pairs in the graph (not shown, assuming you will identify them).
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Identify the x-values of the options:
- (-6, 0) – x = -6
- (-2, 3) – x = -2
- (-1, 8) – x = -1
- (3, -2) – x = 3
- (10, 6) – x = 10
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Check which x-values are present in the existing ordered pairs.
If any of the x-values from the options (-6, -2, -1, 3, 10) are already in use in the existing graph, they cannot be added. However, if they are not present, then those pairs can be added.
Let's say, hypothetically, that the existing ordered pairs in the graph, for example, are:
- (1, 2)
- (3, 4)
- (5, 6)
In this case, x-values 1, 3, and 5 are already taken. So, you can only add the ordered pairs with x-values -6, -2, -1, and 10, because those do not match with x = 1, 3, or 5.
Please compare the x-values from your graph to these possible options to finalize which two ordered pairs can be added to keep the set as a function.