what is continuity?
In general, continuity is continuousness. In terms of Calculus, continuity is when a function can be drawn on a graph without the need to lift the pencil from the paper. A function is continuous if, on the graph, it has no holes, gaps, or breaks. The rule goes as follows:
In order for a function to be considered continuous, it must meet these requirements:
What is discontinuity?
Discontinuity is exactly what it sounds like, non-continuousness. In Calculus, there are 3 types of discontinuity:
- Asymptotic – a function approaches infinity at a value of x or y
- Point – a function is defined for a specific x-value
- Jump – a function approaches two different values from either side of the discontinuity