Finding the Average Rate of Change in Polynomials

The video tutorial explains the concept of average rate of change of a function over a closed interval. It begins by defining the average rate of change as the change in the function's value divided by the change in x. The tutorial then demonstrates how to calculate this using a table and visualizes the concept by sketching a graph. The average rate of change is shown as the slope of the line connecting two points on the function's graph.

What does a closed interval mean in the context of this problem?

• It includes both boundaries.

• It includes only the upper boundary.

• It excludes both boundaries.

• It includes only the lower boundary.

How can the average rate of change of a function be conceptualized?

• As the product of the function values.

• As the sum of the function values.

• As the difference between the maximum and minimum values of the function.

• As the change in the value of the function divided by the change in x.

What is the value of f(-2) for the given function?

• 8

• 4

• 0

• -8

What is the value of f(3) for the given function?

• 3

• 12

• 27

• 15

What is the change in y over the interval from -2 to 3?

• 10

• 20

• 15

• 5

What is the change in x over the interval from -2 to 3?

• 3

• 7

• 5

• 2

What is the average rate of change of the function over the interval from -2 to 3?

• 4

• 3

• 2

• 1

What does the slope of the line connecting two points on a graph represent in this context?

• The average rate of change of the function.

• The minimum value of the function.

• The maximum value of the function.

• The total change in the function.

At x = -2, what is the value of f(x)?

• 27

• -8

• 15

• 0

At x = 3, what is the value of f(x)?

• 0

• 15

• 27

• -8