Question

Which table represents a linear function?

A two column table with five rows. The first column, x, has the entries, 0, 1, 2, 3. The second column, y, has the entries, 1, 2, 4, 8.

A two column table with five rows. The first column, x, has the entries, 0, 1, 2, 3. The second column, y, has the entries, 0, 1, 3, 6.

A two column table with five rows. The first column, x, has the entries, 0, 1, 2, 3. The second column, y, has the entries, 0, 1, 0, 1.

A two column table with five rows. The first column, x, has the entries, 0, 1, 2, 3. The second column, y, has the entries, 1, 3, 5, 7.

Answer 1

To identify which table represents a linear function, we need to check if the change in \( y \) is consistent when \( x \) increases by 1. For a table to represent a linear function, the difference in \( y \) values should be constant.

Let's examine each table:

1. For the first table:
- \( x \): 0, 1, 2, 3
- \( y \): 1, 2, 4, 8
- Differences in \( y \): \( 2 - 1 = 1 \), \( 4 - 2 = 2 \), \( 8 - 4 = 4 \)
- The differences are not consistent (1, 2, 4).

2. For the second table:
- \( x \): 0, 1, 2, 3
- \( y \): 0, 1, 3, 6
- Differences in \( y \): \( 1 - 0 = 1 \), \( 3 - 1 = 2 \), \( 6 - 3 = 3 \)
- The differences are not consistent (1, 2, 3).

3. For the third table:
- \( x \): 0, 1, 2, 3
- \( y \): 0, 1, 0, 1
- Differences in \( y \): \( 1 - 0 = 1 \), \( 0 - 1 = -1 \), \( 1 - 0 = 1 \)
- The differences are not consistent (1, -1, 1).

4. For the fourth table:
- \( x \): 0, 1, 2, 3
- \( y \): 1, 3, 5, 7
- Differences in \( y \): \( 3 - 1 = 2 \), \( 5 - 3 = 2 \), \( 7 - 5 = 2 \)
- The differences are consistent (2, 2, 2).

The fourth table represents a linear function.