Which set of ordered pairs represents a function?

Question

Answer
Multiple Choice Answers
left curly bracket, left bracket, 2, comma, 6, right bracket, comma, left bracket, 2, comma, 3, right bracket, comma, left bracket, 0, comma, minus, 8, right bracket, comma, left bracket, 9, comma, minus, 5, right bracket, right curly bracket{(2,6),(2,3),(0,−8),(9,−5)}
left curly bracket, left bracket, 6, comma, 0, right bracket, comma, left bracket, 7, comma, 2, right bracket, comma, left bracket, 6, comma, 7, right bracket, comma, left bracket, minus, 7, comma, minus, 6, right bracket, right curly bracket{(6,0),(7,2),(6,7),(−7,−6)}
left curly bracket, left bracket, minus, 1, comma, 2, right bracket, comma, left bracket, minus, 7, comma, minus, 8, right bracket, comma, left bracket, minus, 4, comma, 6, right bracket, comma, left bracket, minus, 2, comma, minus, 8, right bracket, right curly bracket{(−1,2),(−7,−8),(−4,6),(−2,−8)}
left curly bracket, left bracket, 0, comma, 5, right bracket, comma, left bracket, 0, comma, minus, 3, right bracket, comma, left bracket, 8, comma, minus, 1, right bracket, comma, left bracket, minus, 8, comma, minus, 3, right bracket, right curly bracket{(0,5),(0,−3),(8,−1),(−8,−3)}

Answer 1

Recall that a set of ordered pairs represents a function if each input (first component of each ordered pair) is associated with exactly one output (second component). If an input is associated with more than one output, then the set of ordered pairs does not represent a function.

Given this definition, let's analyze the sets of ordered pairs provided:

1. {(2,6),(2,3),(0,−8),(9,−5)} – This set does not represent a function because the input '2' is associated with two different outputs: '6' and '3'.

2. {(6,0),(7,2),(6,7),(−7,−6)} – Similarly, this set does not represent a function because the input '6' is associated with two different outputs: '0' and '7'.

3. {(−1,2),(−7,−8),(−4,6),(−2,−8)} – This set represents a function because each input value has a unique output value associated with it.

4. {(0,5),(0,−3),(8,−1),(−8,−3)} – This set does not represent a function because the input '0' is associated with two different outputs: '5' and '−3'.

The correct answer is the third set of ordered pairs:

{(−1,2),(−7,−8),(−4,6),(−2,−8)}