Final answer:
If we add a point to the function that does not follow the pattern of the other ordered pairs, it would no longer function. Adding an ordered pair to the set with an x-value that's already present, such as (-1,5), makes the relation not a function because it gives two outputs for one input.
Step-by-step explanation:
Every term in an expression must have the same dimensions; it does not make sense to add or subtract quantities of differing dimension. In this case, the function is defined using a set of ordered pairs, which means that it represents a continuous mathematical function. If we add a point to the function that does not follow the pattern of the other ordered pairs, it would no longer be a continuous mathematical function.
For example, if we add the point (5, -3) to the function, it would cause it to no longer function because it does not fit the pattern of the other ordered pairs. Adding an ordered pair to the set with an x-value that's already present, such as (-1,5), makes the relation not a function because it gives two outputs for one input.
A function is defined as a relation where each input has exactly one output. In the set of ordered pairs given: {(-4,8), (-1,2), (3,-4), (6,-1), (9,6)}, each x-value (the first number in each pair) is unique, which satisfies the definition of a function. To cause this relation not to be a function, an additional ordered pair with an x-value that is already present in the set would need to be added. For example, if we added the pair (-1,5), this would provide a second output for the input x = -1, which would violate the rule that a function can only have one output for each input.