Exploring Average Rate of Change in Calculus

What is one way to visualize the behavior of a function?

• As a straight line

• As a roller coaster

• As a triangle

• As a circle

What does the slope of a line represent?

• The rate at which the function changes

• The maximum value of the function

• The average value of the function

• The minimum value of the function

How can we approximate the change in a non-linear function?

• By using the average value

• By drawing a line through two points

• By finding the maximum value

• By finding the minimum value

What is required to build a line?

• One point

• Three points

• Two points

• Four points

What does a steeper line indicate about a function?

• The function is increasing rapidly

• The function is increasing slowly

• The function is constant

• The function is decreasing slowly

What does a slope of zero indicate about a function between two points?

• There is no change in the function

• The function is at its maximum

• The function is decreasing

• The function is increasing

What is the average rate of change of a function?

• The total change in the y-direction

• The total change in the x-direction

• The change in the y-direction divided by the change in the x-direction

• The change in the x-direction divided by the change in the y-direction

What does the slope of a line between two points on a function tell us?

• The total change in the function

• The maximum value of the function

• The minimum value of the function

• The average rate of change of the function

What can the average rate of change of a function describe in real-world scenarios?

• The maximum speed of a car

• The minimum speed of a car

• The average speed of a car

• The total distance traveled by a car

What major tool of calculus is introduced to describe how a function changes at a single point?

• Derivative

• Integral

• Limit

• Slope