Bounded
Definition
A function is bounded if its values are limited or restricted within a certain range. It means that the function does not go to infinity or negative infinity.
Analogy
Imagine you have a pet dog and you put up a fence around your backyard. The dog can freely move within the fenced area, but it cannot go beyond the boundaries. Similarly, a bounded function has limits on how high or low its values can be.
Related terms
Unbounded: An unbounded function has no restrictions on its values and can extend infinitely in either positive or negative direction.
Upper Bound: An upper bound of a set of numbers is the maximum value that none of the numbers exceed.
Lower Bound: A lower bound of a set of numbers is the minimum value that none of the numbers fall below.
"Bounded" appears in:
Practice Questions (2)
The base of a solid with square cross sections is bounded by y = \sqrt{x-1}, x = 3, y = 0. What is the function A(x) that can be used to find the volume of this solid when cross-sections are taken perpendicular to the x-axis?
What is the volume of the solid of revolution obtained by rotating the region bounded by the x-axis and the graph of f(x) = x² around the vertical line x = 3?
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