Understanding Functions: Increasing/Decreasing and Concavity

The video tutorial explains how to determine if a function is increasing or decreasing and whether it is concave up or concave down using tables and average rates of change. It provides examples and graphical verification to illustrate these concepts, emphasizing the importance of understanding function behavior in algebra.

What does it mean for a function to be decreasing?

• The function values increase as x increases.

• The function values decrease as x increases.

• The function values remain constant as x increases.

• The function values oscillate as x increases.

How can you determine if a function is concave up?

• The rate of change increases as x increases.

• The rate of change remains constant as x increases.

• The rate of change oscillates as x increases.

• The rate of change decreases as x increases.

What is the significance of a negative average rate of change that is increasing?

• The function is increasing and concave up.

• The function is increasing and concave down.

• The function is decreasing and concave up.

• The function is decreasing and concave down.

In the context of the video, what does a downward facing cup indicate?

• The function is increasing and concave down.

• The function is decreasing and concave up.

• The function is increasing and concave up.

• The function is decreasing and concave down.

What does it mean if the average rates of change are getting larger?

• The function is neither concave up nor down.

• The function is concave up.

• The function is oscillating.

• The function is concave down.

How can you verify the concavity of a function graphically?

• By checking if the graph forms a circle.

• By checking if the graph forms a zigzag pattern.

• By checking if the graph forms an upward or downward facing cup.

• By checking if the graph forms a straight line.

What does an upward facing cup on a graph indicate?

• The function is increasing and concave up.

• The function is decreasing and concave up.

• The function is decreasing and concave down.

• The function is increasing and concave down.

What is the relationship between the rate of change and concavity?

• If the rate of change is constant, the function is concave up.

• If the rate of change is zero, the function is concave up.

• If the rate of change is decreasing, the function is concave up.

• If the rate of change is increasing, the function is concave up.

What does it mean if the function values increase as x increases?

• The function is oscillating.

• The function is constant.

• The function is increasing.

• The function is decreasing.

What is the purpose of finding the average rate of change in this context?

• To determine the symmetry of the function.

• To determine if the function is linear.

• To determine if the function is periodic.

• To determine the concavity of the function.