Answer:
We conclude that if we add (1, 4) to this set, it prevents the set from representing a function.
Step-by-step explanation:
Given the initial function
{(-3, 7), (1, 5), (4, 13)}
We know that the given function indicates the relation in which each input has only one output.
i.e.
at x = -3, y = 7
at x = 1, y = 5
at x = 4,y = 13
Thus, it represents a function, becaus there is no repetitive inputs.
The only way the above function will no longer be a function we bring a point, adding of which makes the initial function having repetitive inputs.
i.e. if we add (1, 4) to the initial set, the relation will no longer be a function.
because induction of the point (1, 4) causes repetitive inputs because x = 1 is already present in the set.
so adding the point (1, 4)
{(-3, 7), (1, 4), (1, 5), (4, 13)}
Now, check the points (1, 4) and (1, 5).
It is clear that there are multiple outputs for x = 1. In other words, the input is no more a unique value as x=1 has been repeated multiple times.
Therefore, we conclude that if we add (1, 4) to this set, it prevents the set from representing a function.
