Question

The average rate of change from x equals -22 to x equals 4 is 34. Which statement best describes the f(x)?

Option 1: The function is decreasing
Option 2: The function is increasing
Option 3: The function is constant
Option 4: The function is undefined

Answer 1

The function is increasing because the average rate of change from x = -22 to x = 4 is positive at 34, indicating the function values rise as x increases. the correct statement about the function f(x) is that it is increasing, which corresponds to Option 2.

Step-by-step explanation:

The average rate of change is determined by finding the slope of a function over a specific interval. In this case, the average rate of change from x = -22 to x = 4 is 34.

This means that for every 1 unit increase in x, the function increases by 34 units on average. Since the average rate of change is positive, the function is increasing.

The average rate of change of a function between two points is calculated as the difference in the function values at these points, divided by the difference in the x-values. In this case, the average rate of change from x = -22 to x = 4 is 34. This means that as x increases from -22 to 4, the function values are increasing at an average rate of 34. Therefore, the function is not decreasing or staying constant; it is increasing. Hence, the correct statement about the function f(x) is that it is increasing, which corresponds to Option 2.