Question

A function is represented by the values in the table.

x y
22 26
20 22
16 20
14 18
10 14
Choose from the drop-down menu to complete the statement.

The function represented in the table
Choose...
linear.

Answer 1

To determine whether the function represented in the table is linear, we can check if the changes in \( y \) for equal changes in \( x \) are consistent.

Calculating the differences in \( y \) values for equal intervals of \( x \):

- From \( x = 10 \) to \( x = 14 \):
- \( 14 - 10 = 4 \)
- \( y \) changes from \( 14 \) to \( 18 \) (increase of \( 4 \))

- From \( x = 14 \) to \( x = 16 \):
- \( 16 - 14 = 2 \)
- \( y \) changes from \( 18 \) to \( 20 \) (increase of \( 2 \))

- From \( x = 16 \) to \( x = 20 \):
- \( 20 - 16 = 4 \)
- \( y \) changes from \( 20 \) to \( 22 \) (increase of \( 2 \))

- From \( x = 20 \) to \( x = 22 \):
- \( 22 - 20 = 2 \)
- \( y \) changes from \( 22 \) to \( 26 \) (increase of \( 4 \))

The differences in \( y \) are not consistent for equal changes in \( x \), thus the function does not have a steady rate of change, which is a characteristic of linear functions.

Based on this analysis, the function represented in the table is **not** linear.

So, the completed statement is:

The function represented in the table is **not** linear.