Question

What is the average rate of change of g(x) over the interval [-1,2]?

a) g(2) - g(-1)
b) [g(2) - g(-1)] / (2 - (-1))
c) g(2) + g(-1)
d) g(2) / g(-1)

Answer 1

The average rate of change of g(x) over the interval [-1,2] is [g(2) - g(-1)] / (2 - (-1)) (Option B).

Step-by-step explanation:

The average rate of change is a measure used to determine how a function's output (or 'y' value) changes on average for each unit change in the input (or 'x' value) over a specified interval.

To compute the average rate of change of a function \( g(x) \) over an interval, you take the difference between the function values at the end of the interval and divide that by the difference in the \( x \)-values (the length of the interval).

Given the interval is [-1, 2], we can calculate the average rate of change as follows:

1. Identify the two x-values that define the interval. In this case, these are ( x₁ = -1 ) and ( x₂ = 2).
2. Find the function values at these two points: g(x₁) = g(-1) and ( g(x₂) = g(2).
3. Compute the difference in function values: g(x₂) - g(x₁) = g(2) - g(-1).
4. Compute the difference in x-values: x₂ - x₁ = 2 - (-1) = 2 + 1 = 3.
5. Calculate the average rate of change by dividing step 3 by step 4: [g(2) - g(-1)] / (2 - (-1)) = [g(2) - g(-1)] /3)

From the options given, the average rate of change of g(x) over the interval [-1, 2] is correctly expressed by the formula: [g(2) - g(-1)] / (2 - (-1))
Therefore, the correct answer is b) [g(2) - g(-1)] / (2 - (-1))