Define Extrema and Boundness of Functions

The video tutorial explains the concept of extrema, including absolute and relative maxima and minima, and how they are represented on graphs. It also covers the concept of boundedness in functions, distinguishing between bounded and unbounded functions, and provides examples of each. The tutorial emphasizes understanding the context of questions related to extrema and boundedness to avoid common mistakes.

What is the main difference between absolute and relative extrema?

• Relative extrema are the highest and lowest points on the entire graph, while absolute extrema are within a specific interval.

• Absolute extrema occur only in polynomial functions, while relative extrema occur in all types of functions.

• Absolute extrema are the highest and lowest points on the entire graph, while relative extrema are within a specific interval.

• Relative extrema are always higher than absolute extrema.

Where does the absolute maximum point occur on a graph?

• At the lowest point the graph reaches.

• At the highest point the graph reaches.

• At the midpoint of the graph.

• At the point where the graph changes direction.

How can you identify a relative maximum on a graph?

• By finding the point that is the highest on the entire graph.

• By finding the point that is higher than its immediate neighbors within a specific interval.

• By finding the point that is the lowest on the entire graph.

• By finding the point that is lower than its immediate neighbors within a specific interval.

What does it mean for a graph to be bounded above?

• The graph has no maximum or minimum points.

• The graph does not go above a certain value.

• The graph does not go below a certain value.

• The graph is symmetrical around the x-axis.

Which of the following is an example of a bounded graph?

• A graph that oscillates indefinitely.

• A graph with no horizontal asymptotes.

• A quadratic function with a maximum point.

• A line that extends infinitely in both directions.

What is a characteristic of an unbounded graph?

• It is always symmetrical.

• It has a horizontal asymptote.

• It continues indefinitely in at least one direction.

• It has a maximum and minimum point.

How can you determine if a function is bounded below?

• If it is a linear function.

• If it does not go below a certain value.

• If it has a maximum point.

• If it has a horizontal asymptote.