Question

Select the function with an average rate of change of 3 over the interval [1, 3].

Answer 1

only the second choice, the graph, fits the required.

Explanation:

The rate of change on [1, 3] is calculated as: [h(3) - h(1)] / 2

For the first set of (x, y) values: h(3) = 6, h(1) = -2, so [6 - (-2)] / 2 = 4.

For the graph, h(3) = 4, h(1) = -2, so [4 - (-2)] / 2 = 3, which is what we need.

For the equation, h(3) = 27/8 - 1 = 19/8, while h(1) = 1/2, so (19/8 - 1/2) / 2 = 15/16.

Answer 2

The average rate of change on [1, 3] is calculated as: [h(3) - h(1)] / 2
For the first set of (x, y) values: h(3) = 6, h(1) = -2, so [6 - (-2)] / 2 = 4.
For the graph, h(3) = 4, h(1) = -2, so [4 - (-2)] / 2 = 3, which is what we need.
For the equation, h(3) = 27/8 - 1 = 19/8, while h(1) = 1/2, so (19/8 - 1/2) / 2 = 15/16.

Therefore only the second choice, the graph, fits the required.