AP Calculus AB Flashcards: Connecting Infinite Limits and Vertical Asymptotes
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 10 cards to help you master important concepts.
A function h(x) has a vertical asymptote at x=5. What must be true about the limit of h(x) as x approaches 5?
The limit of h(x) as x approaches 5 from at least one side (the left or the right) must be either positive infinity or negative infinity.
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A function h(x) has a vertical asymptote at x=5. What must be true about the limit of h(x) as x approaches 5?
The limit of h(x) as x approaches 5 from at least one side (the left or the right) must be either positive infinity or negative infinity.
If you determine that lim (x→-1) g(x) = -∞, what feature does the graph of g(x) have at x=-1?
The graph of g(x) has a vertical asymptote at x=-1, where the function's values decrease without bound as x gets closer to -1.
What does an infinite limit describe?
An infinite limit describes the unbounded behavior of a function, where its values increase or decrease without bound as the input approaches a specific value.
Define a vertical asymptote using the concept of limits.
The line x=c is a vertical asymptote of a function if the limit of the function as x approaches c from the left or the right is either positive or negative infinity.
What does the statement lim (x→c) f(x) = ∞ imply about the graph of f(x)?
This statement implies that the graph of f(x) has a vertical asymptote at x=c, where the function's values increase without bound as x approaches c.
Why is it insufficient to just say a function is 'undefined' at a point to prove a vertical asymptote exists?
A function can be undefined at a point by having a hole, not an asymptote. An infinite limit must be established to prove the function exhibits the unbounded behavior characteristic of an asymptote.
How are limits involving infinity used to interpret a function's behavior?
Limits involving infinity are used to describe and explain the asymptotic and unbounded behavior of a function as it gets closer to a particular input value.
What is meant by the 'unbounded behavior' of a function?
Unbounded behavior refers to a situation where a function's output values increase or decrease without any finite limit as the input approaches a certain number.
How does the concept of a limit extend to include infinite limits?
The concept of a limit is extended to describe cases where a function does not approach a finite number, but instead its output grows infinitely large or small.
What is the relationship between infinite limits and asymptotic behavior?
Infinite limits are the formal mathematical tool used to precisely describe and confirm the existence of vertical asymptotic behavior in a function.