Question

1. a set of ordered pairs is shown below. {( - 1, 2), (3, 4), (0, - 1), (2, 5), (- 1, 6)} which ordered pair should be removed to make the set a function? why? ______

Explanation:

Step1: Recall function definition

A function requires each input (x-value) to have exactly one output (y-value).

Step2: Identify duplicate x-values

Check the set $\{(-1, 2), (3, 4), (0, -1), (2, 5), (-1, 6)\}$. The x-value $-1$ appears twice, paired with $2$ and $6$.

Step3: Determine removable pair

Either $(-1, 2)$ or $(-1, 6)$ must be removed to eliminate the duplicate x-value.

Answer:

Either $(-1, 2)$ or $(-1, 6)$ should be removed.

Why?

A function cannot have one input (x-value) mapped to two different outputs (y-values); the x-value $-1$ is associated with both $2$ and $6$, so removing one of these ordered pairs ensures each x-value has only one corresponding y-value.