Question

answer the questions below to determine what kind of function is depicted in the table below.

x	-1	0	1	2	3

answer attempt 1 out of 2

this function is dropdown: exponential, quadratic, linear, none of the above because ratios of succes...
submit answer

Explanation:

Step1: Calculate the ratios of consecutive \( f(x) \) values.

First, find \( \frac{f(0)}{f(-1)} = \frac{384}{256} = 1.5 \).
Then, \( \frac{f(1)}{f(0)} = \frac{576}{384} = 1.5 \).
Next, \( \frac{f(2)}{f(1)} = \frac{864}{576} = 1.5 \).
Finally, \( \frac{f(3)}{f(2)} = \frac{1296}{864} = 1.5 \).

Step2: Analyze the ratios.

For a function to be exponential, the ratio of consecutive output values (when the input increases by a constant amount, here \( \Delta x = 1 \)) should be constant. Since the ratio \( \frac{f(x + 1)}{f(x)} = 1.5 \) is constant for all consecutive \( x \) values, the function is exponential.

Answer:

exponential