Which set of ordered pairs represents a function?
Answer
Multiple Choice Answers
left curly bracket, left bracket, minus, 2, comma, minus, 1, right bracket, comma, left bracket, minus, 5, comma, minus, 8, right bracket, comma, left bracket, 1, comma, 0, right bracket, comma, left bracket, 5, comma, minus, 1, right bracket, right curly bracket{(−2,−1),(−5,−8),(1,0),(5,−1)}
left curly bracket, left bracket, 5, comma, minus, 3, right bracket, comma, left bracket, 5, comma, 4, right bracket, comma, left bracket, minus, 1, comma, minus, 7, right bracket, comma, left bracket, minus, 6, comma, 0, right bracket, right curly bracket{(5,−3),(5,4),(−1,−7),(−6,0)}
left curly bracket, left bracket, 2, comma, minus, 9, right bracket, comma, left bracket, 6, comma, 8, right bracket, comma, left bracket, minus, 9, comma, 4, right bracket, comma, left bracket, 6, comma, minus, 1, right bracket, right curly bracket{(2,−9),(6,8),(−9,4),(6,−1)}
left curly bracket, left bracket, 7, comma, 8, right bracket, comma, left bracket, 5, comma, minus, 4, right bracket, comma, left bracket, 3, comma, 5, right bracket, comma, left bracket, 5, comma, minus, 6, right bracket, right curly bracket{(7,8),(5,−4),(3,5),(5,−6)}
A set of ordered pairs represents a function if each input (the first component of each ordered pair) corresponds to exactly one output (the second component). In other words, in a function, each x-value must be paired with only one y-value.
Let's look at the options to identify which set of ordered pairs satisfies this condition:
1. {(−2,−1),(−5,−8),(1,0),(5,−1)}
In this set, all the x-values (inputs) are unique and thus each corresponds to only one y-value (output). This set represents a function.
2. {(5,−3),(5,4),(−1,−7),(−6,0)}
Here, the x-value 5 appears twice and is paired with two different y-values (−3 and 4). This violates the definition of a function, so this set of ordered pairs does not represent a function.
3. {(2,−9),(6,8),(−9,4),(6,−1)}
Similar to the second option, the x-value 6 is paired with two different y-values (8 and −1), which means that this set does not represent a function either.
4. {(7,8),(5,−4),(3,5),(5,−6)}
Again, the x-value 5 appears twice with two different y-values (−4 and −6), indicating this set is not a function.
The only set of ordered pairs that represents a function is:
{(−2,−1),(−5,−8),(1,0),(5,−1)}