AP Calculus AB Flashcards: Confirming Continuity over an Interval
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.
What single condition must be met for a function to be declared 'continuous on an interval'?
The function must be proven to be continuous at every individual point that makes up the interval.
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What single condition must be met for a function to be declared 'continuous on an interval'?
The function must be proven to be continuous at every individual point that makes up the interval.
State the general rule for the continuity of common function types.
Polynomial, rational, power, exponential, logarithmic, and trigonometric functions are continuous on all points in their domains.
What is the relationship between a function's domain and its interval of continuity for the main function families?
For polynomial, rational, power, exponential, logarithmic, and trigonometric functions, the interval of continuity is the same as the function's domain.
List three types of functions that are continuous wherever they are defined.
Three examples are logarithmic, trigonometric, and power functions, which are all continuous on their domains.
What is the first step to determine the interval over which a rational function is continuous?
The first step is to determine the function's domain, as rational functions are continuous at all points in their domain.
Are trigonometric functions, like sin(x) or tan(x), continuous?
Yes, trigonometric functions are continuous at all points in their respective domains.
What is the interval of continuity for any polynomial function?
Since polynomial functions are continuous on their domains and their domain is all real numbers, they are continuous everywhere.
How do you confirm continuity over an interval for a given function?
You must determine the intervals where the function is defined (its domain) and confirm it is continuous at each point within those intervals.
If you know the domain of an exponential function, what do you know about its continuity?
You know that the function is continuous over its entire domain.
What does it mean for a function to be continuous on an interval?
A function is continuous on an interval if it is continuous at each point within that interval.