Step 1. We are given a graph with 4 points and we need to select which of the options can be added to the graph so that the point will still represent a function.
The points we have are:
Step 2. The rule so that the set of points (x,y) represent a function is:
This means that we cannot have different y-values for just one x-value.
Step 3.
Analyzing the options:
(-2,3) --> We already have a point that is (-2,-2) so if we include this point we will have another y-value (3) for the same x-value of -2. Therefore, this is not the answer.
A similar thing happens with the points
(3,0) and (-2,0) --> We already have a point that is (3,1) so we cannot include (3,0) and we cannot include (-2,0) for the same reason we could not include (-2,3)
Therefore, the only correct choice is:
(0,3) Because we don't have already any point at x=0 and will not be repeating it or having more than one y-value for the same x-value.
Answer:
(0, 3)