Question

Decide whether the data in the table represent a linear function or an

exponential function. Explain how you know.
y
1
16
2
8
3
0
4
-8
5
-16
A. The data represent an exponential function because there is a
common ratio of 2.
B. The data represent a linear function because there is a common
difference of 8.
OC. The data represent a linear function because there is a common
difference of -8.
D. The data represent an exponential function because there is a
common ratio of 1

Answer 1

The data in the table represent a linear function because there is a common difference of -8.

Step-by-step explanation:

The data in the table represent a linear function because there is a common difference of -8. In a linear function, the change in the dependent variable (y) is constant for every change in the independent variable (x).

Let's examine the differences between consecutive values of y:

• 16 - 1 = 15
• 8 - 16 = -8
• 0 - 8 = -8
• -8 - 0 = -8
• -16 - (-8) = -8

As you can see, there is a consistent difference of -8 between each pair of values, indicating a linear relationship.