Bounded functions

The video tutorial explains the concept of boundedness in mathematical graphs, including bounded above, bounded below, and unbounded graphs. It provides examples using different types of functions: a polynomial, a semicircle, and a rational function. The tutorial aims to help students understand how to identify boundedness in graphs and offers practical examples to illustrate these concepts.

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

• The graph does not go above a certain value.

• The graph has no maximum or minimum values.

• The graph extends to infinity in both directions.

• The graph does not go below a certain value.

In the context of boundedness, what is an absolute maximum?

• A point where the graph changes direction.

• A point where the graph is undefined.

• The highest point on the graph.

• The lowest point on the graph.

Which of the following describes a function that is both bounded above and below?

• The graph has both a maximum and a minimum.

• The graph has no maximum or minimum.

• The graph has a maximum but no minimum.

• The graph extends to infinity in both directions.

What type of graph is described as unbounded?

• A graph that is a straight line.

• A graph that extends to infinity in both directions.

• A graph that has a maximum and a minimum.

• A graph that is a semicircle.

Which of the following functions is not bounded?

• A function with a defined range.

• A function that extends to infinity in both directions.

• A semicircle with a maximum and minimum value.

• A polynomial function with a maximum value.