Which set of ordered pairs demonstrates a function?
A
(-2, -4), (-1, -2), (1, 2), (2, 4)
B
(-2, 4), (1, 2), (1, -2), (2, -4)
C
(-2, 4), (-1, 2), (-1, 2), (-2, -4)
D
(-2, 4), (-1, 2), (-1, -2), (-2, -4)
To determine which set of ordered pairs demonstrates a function, we need to check if each input value (x-coordinate) corresponds to a unique output value (y-coordinate). In other words, each x-value from the set should only appear once and should not be repeated with different y-values.
Let's analyze each set of ordered pairs:
A: (-2, -4), (-1, -2), (1, 2), (2, 4)
In this set, each x-value appears only once (no repetition) and has a unique y-value associated with it. Therefore, it demonstrates a function.
B: (-2, 4), (1, 2), (1, -2), (2, -4)
In this set, the x-value of 1 appears twice, with different y-values (-2 and 2). Therefore, it does not demonstrate a function.
C: (-2, 4), (-1, 2), (-1, 2), (-2, -4)
In this set, the x-value of -1 appears twice, with the same y-value (2). Therefore, it does not demonstrate a function.
D: (-2, 4), (-1, 2), (-1, -2), (-2, -4)
In this set, there are no repetitions of x-values, and each x-value has a unique y-value associated with it. Therefore, it demonstrates a function.
Thus, the set of ordered pairs that demonstrates a function is A: (-2, -4), (-1, -2), (1, 2), (2, 4).