To determine which ordered pair can be plotted together with the four points (−4, 2), (−2, −3), (2, 3), and (3, −1) while still representing a function, we must remember the definition of a function. A function can have only one output (y-value) for each input (x-value).
Let's analyze the x-coordinates of the given points:
- (−4, 2) has x = −4
- (−2, −3) has x = −2
- (2, 3) has x = 2
- (3, −1) has x = 3
The x-coordinates of the points are −4, −2, 2, and 3. For the graph to still represent a function, any new point added should have an x-coordinate that is not one of these existing x-coordinates.
So, we can choose any x-coordinate that is not −4, −2, 2, or 3. For example, any of the following points would keep the graph as a function:
- (1, any y-value)
- (0, any y-value)
- (−1, any y-value)
If we select, for instance, (1, 5), this would not conflict with any existing points, thus maintaining the function's definition.
Therefore, any point with an x-coordinate not equal to −4, −2, 2, or 3 will work. An example ordered pair we can choose is (1, 5).