Final answer:
The set of ordered pairs could have been generated by a linear function.
Step-by-step explanation:
The set of ordered pairs (-3,-3), (-2,0), (-1,3), (0,6), (1,9), (2,12) could have been generated by a linear function. To determine this, we can examine if the relationship between the x-values and y-values is constant. If the change in y-values for each change in x-values is the same, then it is a linear function. Let's calculate the differences in y-values for each pair of consecutive x-values:
(-2,0) - (-3,-3), difference in y-values = 0 - (-3) = 3
(-1,3) - (-2,0), difference in y-values = 3 - 0 = 3
(0,6) - (-1,3), difference in y-values = 6 - 3 = 3
(1,9) - (0,6), difference in y-values = 9 - 6 = 3
(2,12) - (1,9), difference in y-values = 12 - 9 = 3
As we can see, for each change in x-values, the change in y-values is always 3. Therefore, the set of ordered pairs (-3,-3), (-2,0), (-1,3), (0,6), (1,9), (2,12) can be generated by a linear function.