Continuity
Definition
Continuity describes whether or not there are any breaks, holes, or jumps in a function. A continuous function has no interruptions and can be drawn without lifting your pen from the paper.
Analogy
Think of continuity as driving on a smooth road with no potholes or speed bumps. You can smoothly travel along the path without any sudden disruptions.
Related terms
Discontinuity: Discontinuity occurs when there are breaks, holes, or jumps in a function.
Intermediate Value Theorem (IVT): The IVT states that if you have two points on either side of some value within an interval where a continuous function exists, then there must be at least one point within that interval where the function takes on every value between those two points.
Removable Discontinuity: A removable discontinuity is when there's initially an interruption in the graph of a function but can be fixed by redefining its value at that particular point.
"Continuity" appears in:
Study guides (4)
Additional resources (3)
Practice Questions (3)
- What is true regarding continuity at a point?
- What is the definition of continuity over an open interval?
- Which condition is required to confirm continuity over a closed interval [a, b]?
Resources
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