Unbounded Behavior
Definition
Unbounded behavior refers to the behavior of a function as the input approaches infinity or negative infinity. It describes how a function grows or decreases without any limit.
Analogy
Imagine you have a rocket that is launched into space. As it goes higher and higher, it keeps accelerating without any limit. The speed of the rocket represents the unbounded behavior of a function.
Related terms
Asymptote: A line that a graph approaches but never touches. It can be horizontal, vertical, or slanted.
Infinite Limit: When the limit of a function does not exist because it either approaches positive or negative infinity.
Divergence: When a sequence or series does not approach a finite value but instead grows infinitely large or becomes infinitely small.
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