Question

Decide whether the data in the table represent a linear function or an exponential function. Explain how you know.

У

16
2
8
3
0
4
-8
5
- 16
A. The data represent a linear function because there is a common difference of 8.
B. The data represent a linear function because there is a common difference of -8.
C. The data represent an exponential function because there is a common ratio of 2.
D. The data represent an exponential funetion because there is a

Answer 1

The correct answer is: A. The data represent a linear function because there is a common difference of 8.

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

An exponential function has a constant ratio between consecutive terms. We can calculate the ratios between the successive y-values:

8 / 16 = 0.5

0 / 8 = 0

-8 / 0 = undefined

-16 / (-8) = 2

Here, we see that the ratios are consistently 2, except between 0 and -8 where division by zero occurs. This is a strong indication that the function is exponential.

The values in the table increase by 8 each time, indicating a constant rate of change, which is a characteristic of a linear function.

Therefore, the correct answer is: A. The data represent a linear function because there is a common difference of 8.