Which set of ordered pairs represents a function?

Question

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

Answer 1

A set of ordered pairs represents a function if for every unique first element (often referred to as x in the context of functions), there is only one corresponding second element (often referred to as y). In other words, a function can't have two different output values for the same input value.

Let's examine each set of ordered pairs:

1. {(−4,−7),(8,7),(8,2),(−8,−4)}

In this set, the input 8 has two different outputs: 7 and 2. This violates the definition of a function.

2. {(7,6),(−1,8),(−8,0),(−1,−2)}

In this set, the input −1 has two different outputs: 8 and −2. This violates the definition of a function.

3. {(2,8),(−4,1),(5,0),(−8,1)}

In this set, each input is paired with exactly one output. The inputs 2, −4, 5, and −8 each have only one corresponding output value. This meets the definition of a function.

4. {(2,4),(2,−8),(−5,0),(4,−6)}

In this set, the input 2 has two different outputs: 4 and −8. This violates the definition of a function.

The correct answer is the third set: {(2,8),(−4,1),(5,0),(−8,1)}, as it represents a function.