Exploring Average Rate of Change in Functions

What does the function d(t) represent in the context of the video?

• Acceleration as a function of time

• Speed as a function of distance

• Distance as a function of time

• Time as a function of distance

What is the slope of the line representing the function d(t) = 3t + 1?

• 2 meters per second

• 4 meters per second

• 3 meters per second

• 1 meter per second

How does the rate of change behave in a linear function?

• It decreases over time

• It increases over time

• It remains constant

• It fluctuates randomly

What is the term used to describe the slope of a line that just touches a curve at one point?

• Parallel line

• Tangent line

• Secant line

• Perpendicular line

What concept will be studied in more depth in differential calculus?

• Linear functions

• Average rate of change

• Instantaneous rate of change

• Constant rate of change

What is the average rate of change from t = 0 to t = 1 for the given function?

• 1 meter per second

• 2 meters per second

• 3 meters per second

• 4 meters per second

What is a secant line?

• A line that intersects a curve at two points

• A line that intersects a curve at one point

• A line that is parallel to a curve

• A line that is perpendicular to a curve

What is the average rate of change from t = 2 to t = 3 for the given function?

• 1 meter per second

• 5 meters per second

• 7 meters per second

• 3 meters per second

How does the average rate of change from t = 2 to t = 3 compare to that from t = 0 to t = 1?

• It fluctuates

• It is higher

• It is the same

• It is lower

What happens when you take the slope of the secant line of closer and closer points?

• The slope remains constant

• The slope becomes undefined

• You get closer to the slope of the tangent line

• You get further from the slope of the tangent line