Question

From the table below, determine whether the data shows an exponential function. Explain why or why not.

x
3
2
1
–1
y
8
2
0.5
0.125
a. No; the domain values are at regular intervals and the range values have a common factor 0.25. b. No; the domain values are not at regular intervals although the range values have a common factor. c. Yes; the domain values are at regular intervals and the range values have a common factor 4. d. Yes; the domain values are at regular intervals and the range values have a common factor 0.25.

Answer 1

9514 1404 393

Answer:

b. No; the domain values are not at regular intervals although the range values have a common factor.

Explanation:

The differences between x-values are ...

-1, -1, -1, -2 . . . . not a constant difference

The ratios of y-values are ...

2/8 = 0.5/2 = 0.125/0.5 = 0.25 . . . . a constant difference

The fact that the domain values do not have a common difference renders the common factor of the range values irrelevant. The relation is not exponential.