Master How to determine the boundness of a function

The video tutorial explains how to determine if a function is bounded, bounded above, bounded below, or not bounded. It introduces the concept of boundaries in graphs and provides examples using different types of functions: square root, reciprocal, trigonometric, and piecewise. Each example illustrates whether the function is bounded or not, and in which direction. The tutorial concludes with a summary of how to assess the boundedness of a function.

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

• The function is both bounded above and below.

• The function has no restrictions on its values.

• The function cannot go below a certain minimum value.

• The function cannot exceed a certain maximum value.

Which type of function is described as having no restrictions on how high or low it can go?

• Square root function

• Reciprocal function

• Trigonometric function

• Piecewise function

What characteristic of trigonometric functions makes them bounded?

• They repeat in a cyclical pattern.

• They have asymptotes.

• They are piecewise functions.

• They are always increasing.

In the context of the video, what is a piecewise function?

• A function that is only bounded below.

• A function that is not bounded.

• A combination of different functions.

• A function that is only bounded above.

Why is the piecewise function described as bounded above but not below?

• It has a maximum value it cannot exceed.

• It continues to decrease indefinitely to the right.

• It is a combination of bounded and unbounded functions.

• It has a minimum value it cannot go below.