On a coordinate plane, solid circles appear at the following points: (negative 5, negative 3), (negative 4, negative 4), (negative 2, 2), (1, 3), (1, negative 2), (2, 1), (5, negative 4).

Question

Which ordered pair can be removed so that the resulting graph represents a function?

(–2, 2)
(1, 3)
(5, –4)
(–4, –4)

Answer 1

To determine which ordered pair can be removed so that the resulting graph represents a function, we need to remember that a function is defined as a relation where each input (or x-value) corresponds to exactly one output (or y-value). This means that no two points can have the same x-coordinate.

Looking at the provided points:

• (–5, –3)
• (–4, –4)
• (–2, 2)
• (1, 3)
• (1, –2) (This is important as it has the same x-coordinate as another point)
• (2, 1)
• (5, –4)

We see that the x-coordinate 1 appears for two points: (1, 3) and (1, –2). This means we have two different outputs (3 and -2) for the same input (1).

Now, let's evaluate the options given:

1. (–2, 2): This point has a unique x-coordinate (-2).
2. (1, 3): This point shares the x-coordinate (1) with (1, -2).
3. (5, –4): This point has a unique x-coordinate (5).
4. (–4, –4): This point has a unique x-coordinate (-4).

Since (1, 3) and (1, -2) share the same x-value, removing either of these points will allow the graph to represent a function.

Thus, removing either (1, 3) or (1, -2) is correct, but since (1, 3) is one of our options, we take that.

Therefore, the ordered pair that can be removed so that the resulting graph represents a function is:

(1, 3)