Which set of ordered pairs does not represent a function?

Question

Answer
Multiple Choice Answers
left curly bracket, left bracket, 3, comma, 1, right bracket, comma, left bracket, minus, 9, comma, minus, 1, right bracket, comma, left bracket, 0, comma, 6, right bracket, comma, left bracket, minus, 3, comma, 1, right bracket, right curly bracket{(3,1),(−9,−1),(0,6),(−3,1)}
left curly bracket, left bracket, 2, comma, 8, right bracket, comma, left bracket, minus, 9, comma, 9, right bracket, comma, left bracket, 5, comma, minus, 3, right bracket, comma, left bracket, 3, comma, minus, 9, right bracket, right curly bracket{(2,8),(−9,9),(5,−3),(3,−9)}
left curly bracket, left bracket, 6, comma, minus, 8, right bracket, comma, left bracket, 0, comma, minus, 6, right bracket, comma, left bracket, minus, 4, comma, minus, 8, right bracket, comma, left bracket, 2, comma, 3, right bracket, right curly bracket{(6,−8),(0,−6),(−4,−8),(2,3)}
left curly bracket, left bracket, 3, comma, 2, right bracket, comma, left bracket, 5, comma, minus, 1, right bracket, comma, left bracket, 5, comma, 4, right bracket, comma, left bracket, minus, 1, comma, minus, 6, right bracket, right curly bracket{(3,2),(5,−1),(5,4),(−1,−6)}

Answer 1

A set of ordered pairs represents a function if, for every unique x-value (first element of the pair), there is one and only one y-value (second element of the pair) associated with it. In other words, an x-value cannot be paired with more than one distinct y-value.

Let's examine each set of ordered pairs:

1. {(3,1),(−9,−1),(0,6),(−3,1)}
All the x-values are unique, so this set represents a function.

2. {(2,8),(−9,9),(5,−3),(3,−9)}
All the x-values are unique, so this set represents a function as well.

3. {(6,−8),(0,−6),(−4,−8),(2,3)}
All the x-values are unique, so this set represents a function.

4. {(3,2),(5,−1),(5,4),(−1,−6)}
In this set, the x-value 5 is paired with two different y-values (−1 and 4). This violates the definition of a function as each x-value must be paired with exactly one y-value.

Therefore, the set that does not represent a function is:

{(3,2),(5,−1),(5,4),(−1,−6)}