Answer:
Table 2.
Explanation:
Recall that by definition, a linear function increases linearly. That is, the rate of change between any two points is constant.
We can go through each table and verify its rate of change.
Table 1)
For Table 1, note that y = -19 when x = 0.
When x = 1, y = -11. In other words, we added 8 for every increase of one for x.
When x = 2, y = -3. We still increased by 8 for every increase of one for x.
When x = 3, y = 5. Since -3 + 8 = 5, all points in Table 1 shows a constant rate of change.
In conclusion, Table 1 represents a linear function.
Table 2)
For Table 2, note that y = -1.5 when x = 0.
When x = 1, y = -1.5. In other words, we increased by 3 for every increase of one for x.
However, when x = 2, y = 3. This time, we only increased by 1.5 for every increase of one for x. Since the two rates are not equivalent, Table 2 is nonlinear.
Table 3)
Again, note that for Table 3, y = 15 when x = 0.
When x = 1, y = 12. So, we decreased by 3 for every increase of one for x.
When x = 2, y = 9. And when x = 3, y = 6. For both cases, we still decreased by 3 for every increase of one for x.
In conclusion, Table 3 represents a linear function.
Therefore, the table that represents a nonlinear function is Table 2.