The relationship between x-values and y-values can be defined, in some cases, by a function. Which set of x and y coordinate pairs is NOT a function?
Responses
{(−2, −2), (−1, −2), (0, −2), (1, −2), (2, −2)}
{(−2, −2), (−1, −2), (0, −2), (1, −2), (2, −2)}
{(0, 0), (4, 15), (6, 17), (7, 20), (10, 27)}
{(0, 0), (4, 15), (6, 17), (7, 20), (10, 27)}
{(0, 4), (1, 0), (−1, −2), (2, 3), (2, −3)}
{(0, 4), (1, 0), (−1, −2), (2, 3), (2, −3)}
{(−2, 4), (2, 4), (1, 4), (3, 4), (5, 4)}
{(0, 4), (1, 0), (−1, −2), (2, 3), (2, −3)}
To determine whether a given set of coordinate pairs is a function, we need to check if each x-value is associated with only one y-value.
Let's analyze the sets one by one:
Set 1: {(−2, −2), (−1, −2), (0, −2), (1, −2), (2, −2)}
In this set, every x-value is associated with the y-value -2. Since each x-value has the same y-value, this is a function.
Set 2: {(0, 0), (4, 15), (6, 17), (7, 20), (10, 27)}
In this set, each x-value is associated with a different y-value. For example, x=0 is associated with y=0, x=4 is associated with y=15, and so on. Since each x-value has a unique y-value, this is a function.
Set 3: {(0, 4), (1, 0), (−1, −2), (2, 3), (2, −3)}
In this set, we can see that x=2 is associated with both y=3 and y=-3, violating the definition of a function. Therefore, this set is not a function.
Set 4: {(−2, 4), (2, 4), (1, 4), (3, 4), (5, 4)}
In this set, every x-value is associated with the y-value 4. Since each x-value has the same y-value, this is a function.
Thus, the set of coordinate pairs that is NOT a function is:
{(0, 4), (1, 0), (−1, −2), (2, 3), (2, −3)}