The graph represents a function.

The graph shows a coordinate plane with 4 points at the following coordinates: (negative 4, 2); (negative 2, negative 3); (2, 3); (3, negative 1).

Which ordered pair can be plotted together with these four points, so that the resulting graph still represents a function?

1 answer

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).