Question

Choose all of the sets of points that define non-linear functions. IT IS NOT ALL OF THEM
Responses
A (−4, 0), (−3, 3), (−2, 6), (−1, 0)(−4, 0), (−3, 3), (−2, 6), (−1, 0)
B (−4, 16), (−2, 4), (2, 4), (4, 16)(−4, 16), (−2, 4), (2, 4), (4, 16)
C (−4, −10), (−2, −8), (2, −4), (4, −2)(−4, −10), (−2, −8), (2, −4), (4, −2)
D (−4, −1), (−2, 1), (2, 5), (4, 7)

Answer 1

To determine which sets of points define non-linear functions, we need to check if the points can be connected by a straight line (linear) or not (non-linear).

1. **Set A**: (−4, 0), (−3, 3), (−2, 6), (−1, 0)
- This set does not represent a linear function as the points do not lie on a straight line. Hence, it is non-linear.

2. **Set B**: (−4, 16), (−2, 4), (2, 4), (4, 16)
- This set of points lies on a parabola (y = x² function), so it is non-linear.

3. **Set C**: (−4, −10), (−2, −8), (2, −4), (4, −2)
- The change in y-values is consistent with a linear function (the slope is the same). Thus, this set of points is linear.

4. **Set D**: (−4, −1), (−2, 1), (2, 5), (4, 7)
- The differences in y-values over equal intervals of x-values indicate a consistent slope, which defines a linear function.

Based on this analysis, the sets of points that define non-linear functions are:

**A and B.**