Question

On a coordinate plane, solid circles appear at the following points: (-5, -3), (-4, -4), (-2, 2), (1, 3), (1, -2), (2, 1), (5, -4). Which ordered pair can be removed so that the resulting graph represents a function?

a. (-2, 2)
b. (1, 3)
c. (5, -4)
d. (-4, -4)

Answer 1

The ordered pair that can be removed so that the resulting graph represents a function is (1, 3) (option b), as it causes the x-value '1' to be associated with two different y-values.

Step-by-step explanation:

To determine which ordered pair can be removed so that the resulting graph represents a function, we need to understand the definition of a function in a coordinate system: each x-value must be paired with exactly one y-value. Looking at the given points, (-5, -3), (-4, -4), (-2, 2), (1, 3), (1, -2), (2, 1), (5, -4), we notice that the x-value '1' is paired with two different y-values (3 and -2). Therefore, one of these points needs to be removed to meet the criterion of a function.

The ordered pair (1, 3) or (1, -2) must be removed to ensure that there is only one y-value for each x-value. Since (1, 3) is an option provided, we choose (1, 3) as the ordered pair that can be removed.