Which set of ordered pairs represents a function?
Answer
Multiple Choice Answers
left curly bracket, left bracket, 1, comma, 2, right bracket, comma, left bracket, minus, 6, comma, 2, right bracket, comma, left bracket, minus, 3, comma, minus, 3, right bracket, comma, left bracket, 2, comma, 0, right bracket, right curly bracket{(1,2),(−6,2),(−3,−3),(2,0)}
left curly bracket, left bracket, 8, comma, 9, right bracket, comma, left bracket, minus, 6, comma, minus, 9, right bracket, comma, left bracket, minus, 3, comma, minus, 2, right bracket, comma, left bracket, minus, 3, comma, minus, 5, right bracket, right curly bracket{(8,9),(−6,−9),(−3,−2),(−3,−5)}
left curly bracket, left bracket, minus, 2, comma, minus, 2, right bracket, comma, left bracket, minus, 7, comma, 8, right bracket, comma, left bracket, minus, 7, comma, minus, 2, right bracket, comma, left bracket, 3, comma, 2, right bracket, right curly bracket{(−2,−2),(−7,8),(−7,−2),(3,2)}
left curly bracket, left bracket, 6, comma, minus, 5, right bracket, comma, left bracket, 0, comma, 7, right bracket, comma, left bracket, minus, 1, comma, minus, 1, right bracket, comma, left bracket, 0, comma, 6, right bracket, right curly bracket{(6,−5),(0,7),(−1,−1),(0,6)}
A set of ordered pairs represents a function if each input (or x-coordinate) corresponds to exactly one output (or y-coordinate). In other words, in a function, each x-value must be paired with only one y-value.
Let's evaluate each set of ordered pairs:
1. {(1,2),(−6,2),(−3,−3),(2,0)}
Each x-coordinate is unique, so this set represents a function.
2. {(8,9),(−6,−9),(−3,−2),(−3,−5)}
The x-value −3 corresponds to two different y-values (−2 and −5), so this set does not represent a function.
3. {(−2,−2),(−7,8),(−7,−2),(3,2)}
Similarly, the x-value −7 is paired with two different y-values (8 and −2), so this set also does not represent a function.
4. {(6,−5),(0,7),(−1,−1),(0,6)}
The x-value 0 is paired with two different y-values (7 and 6), which means this set is not a function.
Based on this analysis, the set of ordered pairs that represents a function is:
{(1,2),(−6,2),(−3,−3),(2,0)}