How does the boundedness of a function relate to its graph?

Question

Serenity Johnson · Accepted Answer

If the function is unbounded, the graph would progress to infinity, in some direction(s).

Theodore Amidon · Answer

undefined The boundedness of a function indicates the range of values that the function can take. A function is said to be bounded if its output values are limited within a certain range.

For example, if a function is bounded above, it means that there exists a maximum value that the function can attain. Similarly, if a function is bounded below, it means that there exists a minimum value that the function can attain.

The graph of a bounded function will reflect this limitation in its behavior. For a function bounded above, the graph will not extend indefinitely upwards; rather, it will have a maximum point beyond which it does not rise. Similarly, for a function bounded below, the graph will not extend indefinitely downwards; rather, it will have a minimum point beyond which it does not fall.

In essence, the boundedness of a function is directly related to the behavior of its graph, constraining the range of values that the function can achieve as depicted in its graphical representation.