Question

2. Which table of values does NOT represent a linear function?

O
-2
-2
X
-1
-1
0
-1
0
1
2
-2
X y
-2 2
y
-1
1
2
0
-1
1
0
-2
4

Answer 1

To determine which table of values does not represent a linear function, we compare the rate of change in the y-values for a constant change in the x-values. The third table shows a rate of change in the y-values that is inconsistent with the concept of a linear function, where changes in y should be consistent for changes in x.

Step-by-step explanation:

The question is asking which table of values does not represent a linear function. A linear function is represented by a set of points on a graph that, when connected, form a straight line. This means that for any increment in the x-value, the change in the y-value is consistent. To determine which table does not represent a linear function, we must look at the rate of change between the x- and y-values.

• For the first table: From (0, -1) to (1, 2), the change in y is 3 units for a change of 1 unit in x.
• For the second table: From (-2, 2) to (-1, 1), the change in y is -1 unit for a change of 1 unit in x.
• For the third table: From (0, -2) to (1, 4), the change in y is 6 units for a change of 1 unit in x.

The third table shows a change of 6 units in y for a 1 unit change in x, which is inconsistent compared to the previous points. Thus, the third table does not represent a linear function due to the inconsistent rate of change.