Question

Given the function h(x) = 3(5), Section A is from (x = 0) to (x = 1) and Section B is from (x = 2) to (x = 3).

Part A: Find the average rate of change of each section.
A) Section A: 15; Section B: 15
B) Section A: 0; Section B: 0
C) Section A: 5; Section B: 5
D) Section A: 3; Section B: 3

Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other.
A) 5 times; Section B covers a larger interval.
B) 10 times; Section B has a steeper slope.
C) 1 time; Both sections have the same average rate of change.
D) 2 times; Section B covers a smaller interval.

Answer 1

The average rate of change for both Section A and Section B of the function h(x) = 3(5) is 0, as the function is constant and does not change with x. For both sections, the average rate of change remains the same.

Step-by-step explanation:

The average rate of change of a function over an interval measures how much the function's value changes on average for each unit change in the independent variable over that interval. Given the function h(x) = 3(5), the function is constant since it does not depend on x. This means that the value of h(x) is the same for all values of x and is equal to 15.

For Section A, from (x = 0) to (x = 1), the average rate of change is:

(h(1) - h(0)) / (1 - 0) = (15 - 15) / (1 - 0) = 0/1 = 0

For Section B, from (x = 2) to (x = 3), the average rate of change is:

(h(3) - h(2)) / (3 - 2) = (15 - 15) / (1) = 0

Therefore, the correct answer for Part A is:

B) Section A: 0; Section B: 0

For Part B, since both sections have the same average rate of change, the rate of change of Section B is not larger than the rate of change for Section A. The correct answer is:

C) 1 time; Both sections have the same average rate of change.