Which set of ordered pairs does not represent a function?
Answer
Multiple Choice Answers
left curly bracket, left bracket, 4, comma, 1, right bracket, comma, left bracket, minus, 8, comma, 1, right bracket, comma, left bracket, 0, comma, minus, 2, right bracket, comma, left bracket, minus, 6, comma, 2, right bracket, right curly bracket{(4,1),(−8,1),(0,−2),(−6,2)}
left curly bracket, left bracket, 0, comma, 0, right bracket, comma, left bracket, minus, 9, comma, minus, 5, right bracket, comma, left bracket, minus, 4, comma, 7, right bracket, comma, left bracket, minus, 2, comma, 2, right bracket, right curly bracket{(0,0),(−9,−5),(−4,7),(−2,2)}
left curly bracket, left bracket, minus, 1, comma, minus, 8, right bracket, comma, left bracket, minus, 5, comma, minus, 2, right bracket, comma, left bracket, 8, comma, 9, right bracket, comma, left bracket, minus, 5, comma, minus, 4, right bracket, right curly bracket{(−1,−8),(−5,−2),(8,9),(−5,−4)}
left curly bracket, left bracket, 5, comma, 8, right bracket, comma, left bracket, minus, 3, comma, minus, 2, right bracket, comma, left bracket, 6, comma, 8, right bracket, comma, left bracket, 0, comma, 3, right bracket, right curly bracket{(5,8),(−3,−2),(6,8),(0,3)}
To determine which set of ordered pairs does not represent a function, we need to recall the definition of a function:
A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.
In simpler terms, in a function, no two different ordered pairs can have the same first element (x-coordinate) with different second elements (y-coordinates).
Let's examine each set of ordered pairs:
1. {(4,1),(−8,1),(0,−2),(−6,2)}
All the x-coordinates (4, −8, 0, −6) are different, so this set represents a function.
2. {(0,0),(−9,−5),(−4,7),(−2,2)}
All the x-coordinates (0, −9, −4, −2) are different, so this set represents a function.
3. {(−1,−8),(−5,−2),(8,9),(−5,−4)}
Here, the x-coordinate −5 appears twice with different y-coordinates (−2 and −4). This violates the definition of a function, as one input (−5) relates to two different outputs (−2 and −4).
4. {(5,8),(−3,−2),(6,8),(0,3)}
All the x-coordinates (5, −3, 6, 0) are different, so this set represents a function.
The set that does not represent a function is:
3. {(−1,−8),(−5,−2),(8,9),(−5,−4)}
because it has repeated x-coordinates with different y-values.