What term describes the behavior of a function as x grows without bound in either direction?

• A. End Behavior
• B. Limit
• C. Asymptote
• D. Range

Answer: (A)

End behavior describes what the graph does as x becomes very large in either direction. It tells you how f(x) behaves when x → ∞ or x → −∞, capturing the overall trend for large |x|. For example, a function might approach a specific value, rise without bound, or keep oscillating as x grows, and all of that is end behavior.

A limit is a precise value that f(x) approaches at a particular point or at infinity, but end behavior is the broader idea of the overall trend as x gets very large in both directions. An asymptote is a line the graph gets close to, which is related to end behavior but is a specific geometric feature rather than the general description. The range is simply the set of output values, not about how the function behaves for large x.