Understanding Average Rate of Change

The video tutorial explains how to calculate the average rate of change of a function y of x over a given interval. It starts by identifying the initial and final values of x and y, then introduces the concept of delta notation to represent changes. The tutorial walks through the steps to calculate the average rate of change, emphasizing the change in y over the change in x, and concludes with the final result.

What is the interval over which the average rate of change is calculated?

• From -5 to -2

• From -2 to 5

• From 6 to 0

• From 0 to 6

What is the value of y when x is -5?

• -2

• -5

• 6

• 0

What is the value of y when x is -2?

• 0

• 6

• -2

• -5

How do you calculate the average rate of change?

• By adding the change in y and the change in x

• By dividing the change in y by the change in x

• By multiplying the change in y by the change in x

• By dividing the change in x by the change in y

What does the delta symbol (Δ) represent in this context?

• The average of values

• The difference between values

• The sum of values

• The product of values

What is the change in y over the interval?

• 3

• -6

• 6

• -3

What is the change in x over the interval?

• -6

• -3

• 6

• 3

What is the average rate of change of y with respect to x over the interval?

• 1

• 0

• 2

• -2

If x increases by 1, by how much does y change on average?

• Increases by 2

• Decreases by 2

• Increases by 1

• Decreases by 1

What is the significance of the negative sign in the average rate of change?

• It indicates y increases as x decreases

• It indicates y remains constant as x increases

• It indicates y decreases as x increases

• It indicates y increases as x increases