Answer:
(0, 0)
Explanation:
Step 1: Define a Function
Recall that a graphed relation can only be a function if every input (x-value) has exactly one output (y-value), and not the other way around. That is, a function can have the points (2, 3) and (3, 3), but not (2, 3) and (2, 4), for example. This information will be very useful in solving this problem.
Step 2: Take Inventory of the Current Points
Let's first take into account what points we already have plotted. Using the graph, we can see that our current 4 points are (-3, 0), (-1, 1), (1, 2), and (3, 3). Again, the y-values do not really matter here as they can be repeated, but the x-values are what we need to pay attention to, so let's disregard the y-values of the points and just list the x-values as x = -3, -1, 1, and 3.
Step 3: Use this Information to Choose the Correct Answer
We know that in order to still be a function, the point we add must have an x-value that is not among the above list (and if it is, it must be the same exact point - e.g. if one of the options was (-3, 0), then it would technically work, but that is not the case with any of these points so we can ignore this possibility).
We can see that the x-values of the options are x = 1, 3, -3, and 0. Of these options, 1, 3, and -3 are already in our list, so those are not correct. Therefore, the only point that will keep the graphed relation a function is (0, 0). (Don't worry that the graph doesn't look like a straight line, a function is defined as any set of points that has exactly one output for every input - this does not necessarily mean the function follows an equation as we may normally think!)