Which of the following lists of ordered pairs is a function? A.(2, 4), (3, 9), (4, 16), (5, 25) B.(0, 2), (4, 2), (0, –4), (4, –2) C.(1, 1), (2, 3), (1, 5), (4, 7) D.(2, 4), (–2, 4), (3, 9), (–2, –4)
To determine which list of ordered pairs is a function, we need to check if each x-coordinate (first element) corresponds to only one y-coordinate (second element). If there is any repetition of x-coordinate, it means there are multiple y-values for the same x-value, and therefore, it is not a function.
Let's check each option:
A. (2, 4), (3, 9), (4, 16), (5, 25)
In this list, there is no repetition of x-coordinate, so it is a function.
B. (0, 2), (4, 2), (0, –4), (4, –2)
Here, we have (0, 2) and (0, –4), which means there are multiple y-values for x = 0. Therefore, it is not a function.
C. (1, 1), (2, 3), (1, 5), (4, 7)
In this case, we have (1, 1) and (1, 5), which means there are multiple y-values for x = 1. Thus, it is not a function.
D. (2, 4), (–2, 4), (3, 9), (–2, –4)
Here, (2, 4) and (–2, 4) indicate there are multiple y-values for x = -2. Hence, it is not a function.
Therefore, the only option that represents a function is A. (2, 4), (3, 9), (4, 16), (5, 25).
To determine if a list of ordered pairs is a function, we need to check if each input value (x-coordinate) is paired with a unique output value (y-coordinate). If there is any repetition of input values with different output values, then it is not a function.
Let's analyze each list of ordered pairs:
A. (2, 4), (3, 9), (4, 16), (5, 25)
This list shows a relationship where each input (x-coordinate) has a unique output (y-coordinate). For example, 2 is paired with 4, 3 is paired with 9, etc. Therefore, list A represents a function.
B. (0, 2), (4, 2), (0, –4), (4, –2)
In this list, we see that both (0, 2) and (0, -4) have the same input value of 0 but different output values. Since an input value (0) is associated with more than one output value (2 and -4), list B does not represent a function.
C. (1, 1), (2, 3), (1, 5), (4, 7)
Again, we have repetition of input values, specifically (1, 1) and (1, 5). Since the input value 1 is paired with two different output values (1 and 5), this list does not represent a function.
D. (2, 4), (–2, 4), (3, 9), (–2, –4)
Here, we have the repetition of input value -2, with different output values of 4 and -4. Consequently, list D does not represent a function.
Therefore, the only list that represents a function in the given options is A.