Question

Which of these tables represents a non-linear function?
A 2-column table with 4 rows. Column 1 is labeled x with entries 17, 18, 19, 20. Column 2 is labeled y with entries 20, 19, 18, 17.
A 2-column table with 4 rows. Column 1 is labeled x with entries 17, 18, 19, 20. Column 2 is labeled y with entries negative 16, negative 17, negative 18, negative 19.
A 2-column table with 4 rows. Column 1 is labeled x with entries 17, 18, 19, 20. Column 2 is labeled y with entries 16, 17, 19, 20.
A 2-column table with 4 rows. Column 1 is labeled x with entries 17, 18, 19, 20. Column 2 is labeled y with entries negative 20, negative 19, negative 18, negative 17.

Answer 1

To determine which table represents a non-linear function, we need to look for a pattern in how the \(y\) values change with respect to the \(x\) values. A function is considered linear if it can be represented by a straight line, meaning the change in \(y\) is consistent (i.e., the differences between consecutive \(y\) values are constant).

Let's analyze each table:

1. **Table 1:**
- \(x\): 17, 18, 19, 20
- \(y\): 20, 19, 18, 17
- Changes in \(y\): -1, -1, -1 (consistent)
- This is a linear function.

2. **Table 2:**
- \(x\): 17, 18, 19, 20
- \(y\): -16, -17, -18, -19
- Changes in \(y\): -1, -1, -1 (consistent)
- This is a linear function.

3. **Table 3:**
- \(x\): 17, 18, 19, 20
- \(y\): 16, 17, 19, 20
- Changes in \(y\): +1, +2, +1 (not consistent)
- This is a non-linear function.

4. **Table 4:**
- \(x\): 17, 18, 19, 20
- \(y\): -20, -19, -18, -17
- Changes in \(y\): +1, +1, +1 (consistent)
- This is a linear function.

From this analysis, **Table 3** represents a non-linear function, as the differences in the \(y\) values are not consistent.