Question

Removing which point from the coordinate plane would make the graph a function of x?

On a coordinate plane, points are at (negative 2, negative 3), (negative 2, 1), (negative 4, 3), (0, 4), (1, 1), and (2, 3).
(–4, 3)
(–2, 1)
(0, 4)
(1, 1)

Answer 1

To determine which point should be removed from the coordinate plane to make the graph a function of \( x \), we need to recall the definition of a function: each input (or \( x \)-value) can only have one output (or \( y \)-value).

Let's examine the points provided:

1. \( (-2, -3) \)
2. \( (-2, 1) \)
3. \( (-4, 3) \)
4. \( (0, 4) \)
5. \( (1, 1) \)
6. \( (2, 3) \)

The points \( (-2, -3) \) and \( (-2, 1) \) both have the same \( x \)-value of \(-2\) but different \( y \)-values (-3 and 1). This means that removing one of these will make the remaining points function as a function of \( x \).

Now, let’s look at the potential options given:

- (–4, 3)
- (–2, 1)
- (0, 4)
- (1, 1)

The point that needs to be removed to ensure that the graph is a function of \( x \) is either \( (-2, -3) \) or \( (-2, 1) \). Since only point \( (-2, 1) \) is one of the listed options, removing \( (-2, 1) \) will make the graph a function of \( x \).

Therefore, the correct answer is **(–2, 1)**.