If y = 6x − 3, which of the following sets represents possible inputs and outputs of the function, represented as ordered pairs? (4 points)
{(0, 3), (1, −9), (2, −15)}
{(0, −3), (2, 15), (4, 21)}
{(0, −3), (2, 9), (4, 21)}
{(0, 3), (−2, 15), (4, 21)}
To find the possible outputs of the given function, we substitute the x-values into the expression for y.
For the first set of ordered pairs, when x = 0, y = 6(0) - 3 = -3. This matches the first pair in the set {(0, -3)}.
When x = 1, y = 6(1) - 3 = 3. This does not match the second pair in the set {(1, -9)}.
When x = 2, y = 6(2) - 3 = 9. This does not match the third pair in the set {(2, -15)}.
Therefore, the first set of ordered pairs {(0, -3)} is not a possible set of inputs and outputs for the given function.
For the second set of ordered pairs, when x = 0, y = 6(0) - 3 = -3. This matches the first pair in the set {(0, -3)}.
When x = 2, y = 6(2) - 3 = 9. This does not match the second pair in the set {(2, 15)}.
When x = 4, y = 6(4) - 3 = 21. This matches the third pair in the set {(4, 21)}.
Therefore, the second set of ordered pairs {(0, -3), (2, 15), (4, 21)} is a possible set of inputs and outputs for the given function.
For the third set of ordered pairs, when x = 0, y = 6(0) - 3 = -3. This matches the first pair in the set {(0, -3)}.
When x = 2, y = 6(2) - 3 = 9. This matches the second pair in the set {(2, 9)}.
When x = 4, y = 6(4) - 3 = 21. This matches the third pair in the set {(4, 21)}.
Therefore, the third set of ordered pairs {(0, -3), (2, 9), (4, 21)} is a possible set of inputs and outputs for the given function.
For the fourth set of ordered pairs, when x = 0, y = 6(0) - 3 = -3. This matches the first pair in the set {(0, -3)}.
When x = -2, y = 6(-2) - 3 = -15. This matches the second pair in the set {(-2, 15)}.
When x = 4, y = 6(4) - 3 = 21. This matches the third pair in the set {(4, 21)}.
Therefore, the fourth set of ordered pairs {(0, -3), (-2, 15), (4, 21)} is a possible set of inputs and outputs for the given function.
In summary, the possible sets of inputs and outputs (represented as ordered pairs) for the given function are:
{(0, -3)}
{(0, -3), (2, 9), (4, 21)}
{(0, -3), (-2, 15), (4, 21)}
So, the correct answer is {(0, -3), (2, 9), (4, 21)}.