AP Calculus BC 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 is the fundamental condition required to confirm continuity over an interval?
The fundamental condition is that the function must be proven to be continuous at every single point within that interval.
Card 1 of 10
All Flashcards (10)
What is the fundamental condition required to confirm continuity over an interval?
The fundamental condition is that the function must be proven to be continuous at every single point within that interval.
Is continuity at a single point sufficient to establish continuity over an interval containing that point?
No, continuity must be established for each individual point throughout the entire interval.
To find the interval of continuity for a rational function, what is the most important characteristic to consider?
The most important characteristic is the function's domain, as rational functions are continuous at all points in their domain.
Which six types of functions are continuous at all points in their domains?
Polynomial, rational, power, exponential, logarithmic, and trigonometric functions are continuous on all points in their domains.
How do you determine the interval of continuity for a polynomial function?
Since polynomial functions are continuous at all points in their domain and their domain is all real numbers, they are continuous everywhere.
What is the primary objective when analyzing a function for 'continuity over an interval'?
The primary objective is to determine the specific intervals where the function is continuous at every point.
What general rule governs the continuity of logarithmic and exponential functions?
The general rule is that these functions are continuous at all points that are within their respective domains.
What does it mean for a function to be continuous on an interval?
A function is continuous on an interval if the function is continuous at each point in the interval.
If you are asked to determine the intervals over which a trigonometric function is continuous, where should you look for potential discontinuities?
You should look for points where the function is not in its domain, as trigonometric functions are continuous at all points in their domains.
Define 'Intervals of Continuity'.
Intervals of continuity are the specific intervals over which a function is continuous at every point.