Question

Which set of ordered pairs represents a function?

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

Answer 1

A set of ordered pairs represents a function when each x-value is paired with a unique y-value. The set {(7,-2), (5,-9), (-7,-3), (7,4)} represents a function.

Step-by-step explanation:

In order for a set of ordered pairs to represent a function, each x-value (first element in the pair) must be paired with a unique y-value (second element in the pair). Looking at the given options, the set of ordered pairs that represents a function is {(7,-2), (5,-9), (-7,-3), (7,4)} because each x-value is paired with a unique y-value.

The question is asking which set of ordered pairs represents a function. A function in mathematics is a set of ordered pairs where each first element (commonly referred to as 'x' or the input) is associated with exactly one second element (usually 'y' or the output). Therefore, to determine which set represents a function, we must choose the set where no first element is repeated with a different second element.

{(7,−2),(5,−9),(−7,−3),(7,4)} - here the number 7 is repeated as the first element in two pairs, which violates the definition of a function.

{(−3,−8),(−3,−4),(−7,2),(4,−1)} - the number −3 is repeated, so this set is also not a function.

{(5,−4),(−6,6),(6,−4),(3,−6)} - each first element is unique, which fits the definition of a function.

{(−4,7),(−9,9),(7,−1),(7,−4)} - the number 7 is repeated as the first element, not a function.

Therefore, the set of ordered pairs that represents a function is {(5,−4),(−6,6),(6,−4),(3,−6)} because each input or first element is associated with only one output or second element.