Question

Given the function f(x) in the table below:

x 1 2 3 4
Teams f(x) 16 8 4 2

Compute the average rate of change of f(x) from x=1 to x=4 and identify the meaning of that rate.

A. Negative three over fourteen; on average, there were 3 fewer teams every 14 rounds.
B. Negative fourteen over three; on average, there were 14 fewer teams every 3 rounds.
C. 3; there were 3 rounds between rounds 1 and 4.
D. 14; there were 14 fewer teams between rounds 1 and 4.

Answer 1

he average rate of change of f(x) from x=1 to x=4 is -14/3, meaning that on average, there were 14 fewer teams for every increase of 3 rounds, corresponding to option B.

Step-by-step explanation:

The average rate of change of a function is calculated by finding the difference in y-values divided by the difference in x-values between two points on the function. In this case, we are finding the average rate of change of f(x) from x = 1 to x = 4. The difference in y-values is 2 - 16 = -14, and the difference in x-values is 4 - 1 = 3. So, the average rate of change is -14/3, which simplifies to -14/3.

The meaning of this rate is that, on average, there were 14 fewer teams every 3 rounds. Since the rate is negative, it indicates a decrease in the number of teams over time.