Which set of ordered pairs represents a function?
Answer
Multiple Choice Answers
left curly bracket, left bracket, 9, comma, minus, 1, right bracket, comma, left bracket, minus, 3, comma, 0, right bracket, comma, left bracket, 9, comma, minus, 6, right bracket, comma, left bracket, 0, comma, 8, right bracket, right curly bracket{(9,−1),(−3,0),(9,−6),(0,8)}
left curly bracket, left bracket, minus, 7, comma, 8, right bracket, comma, left bracket, 6, comma, 8, right bracket, comma, left bracket, minus, 1, comma, 9, right bracket, comma, left bracket, minus, 1, comma, minus, 9, right bracket, right curly bracket{(−7,8),(6,8),(−1,9),(−1,−9)}
left curly bracket, left bracket, 3, comma, minus, 6, right bracket, comma, left bracket, minus, 5, comma, 8, right bracket, comma, left bracket, 3, comma, 5, right bracket, comma, left bracket, minus, 1, comma, minus, 5, right bracket, right curly bracket{(3,−6),(−5,8),(3,5),(−1,−5)}
left curly bracket, left bracket, 5, comma, 8, right bracket, comma, left bracket, 3, comma, minus, 9, right bracket, comma, left bracket, minus, 9, comma, 8, right bracket, comma, left bracket, minus, 8, comma, 3, right bracket, right curly bracket{(5,8),(3,−9),(−9,8),(−8,3)}
A function is a relation in which each input (the first element of the ordered pairs) is associated with exactly one output (the second element of the ordered pairs). If an input is associated with more than one output, then the set of ordered pairs does not define a function.
Let's go through each set of ordered pairs to determine which one represents a function:
1. {(9,−1),(−3,0),(9,−6),(0,8)}
Here, the input 9 is associated with two different outputs: −1 and −6. Therefore, this set does not represent a function.
2. {(−7,8),(6,8),(−1,9),(−1,−9)}
In this set, the input −1 is associated with two different outputs: 9 and −9. Therefore, this set is also not a function.
3. {(3,−6),(−5,8),(3,5),(−1,−5)}
Again, the input 3 is associated with two different outputs: −6 and 5. Thus, this set does not represent a function.
4. {(5,8),(3,−9),(−9,8),(−8,3)}
This time, each input is associated with exactly one output. Therefore, this set of ordered pairs represents a function.
The correct answer is the fourth set of ordered pairs: {(5,8),(3,−9),(−9,8),(−8,3)}