AP Calculus AB Flashcards: Removing Discontinuities
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.
How do you remove a discontinuity at a point where the limit exists?
You remove the discontinuity by defining or redefining the function's value at that point to be equal to the value of the limit as x approaches that point.
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How do you remove a discontinuity at a point where the limit exists?
You remove the discontinuity by defining or redefining the function's value at that point to be equal to the value of the limit as x approaches that point.
For a piecewise function to be continuous at the point where its rule changes, what must be true about the function's 'pieces'?
The value of the expression defining the function on one side of the boundary must equal the value of the expression defining the other side of the boundary.
How do you solve for a parameter to make a piecewise function continuous at a boundary?
Set the expression defining the function on one side of the boundary equal to the expression on the other side of the boundary, and solve for the parameter.
If a function f(x) has a removable discontinuity at x=c, what value should f(c) be redefined as to make it continuous?
The function's value, f(c), should be redefined to equal the value of the limit of f(x) as x approaches c.
For continuity in a piecewise function at a boundary, what three values must be equal?
The value from the left-side expression, the value from the right-side expression, and the defined value of the function at the boundary must all be equal.
What is the objective when solving for a parameter to make a function continuous?
The objective is to find the value of the parameter that makes the function's limit and its defined value equal at a point of potential discontinuity.
What does it mean to "remove a discontinuity"?
It means to redefine a function's value at a single point to make it continuous there, which is only possible if the limit exists at that point.
Under what condition can a discontinuity in a function's graph be removed?
A discontinuity can be removed if the limit of the function exists at the point of discontinuity.
What is the requirement for a piecewise-defined function to be continuous at a boundary point?
The value of the expression on one side of the boundary must equal the value of the expression on the other side, as well as the function's value at the boundary.
What is the relationship between the limit and the function's value at a point where a discontinuity has been removed?
After removing a discontinuity at a point, the value of the function at that point is defined to be equal to the value of the limit at that same point.