Question

1. the relationship defined by the set of ordered pairs {(0,2), (-2,2), (1,4), (0,-1)} is not a function. which of the ordered pairs listed below, when omitted from this set, will make the resulting set a function. a) (1,4) b) (-2,2) c) (0,-1) d) (4,1)

Explanation:

Step1: Recall the definition of a function

A function is a relation where each input (x - value) has exactly one output (y - value). So, we need to check for duplicate x - values in the given set of ordered pairs \(\{(0,2),(- 2,2),(1,4),(0,-1)\}\).

Step2: Identify the duplicate x - value

In the set, the x - value \(x = 0\) appears twice, with corresponding y - values \(y=2\) (from the pair \((0,2)\)) and \(y = - 1\) (from the pair \((0,-1)\)).

Step3: Determine which ordered pair to omit

To make the set a function, we need to remove one of the ordered pairs with \(x = 0\). Looking at the options, option C is \((0,-1)\) and option A has \(x = 1\) (unique), option B has \(x=-2\) (unique), option D is \((4,1)\) (not in the original set). So, if we omit \((0,-1)\) (or \((0,2)\), but \((0,-1)\) is an option), the remaining set will have each x - value with only one y - value.

Answer:

C. \((0,-1)\)