Answer
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Work Step by Step
Right-continuous, left-continuous, and continuity are concepts related to the behavior of a function at a specific point.
1. Right-Continuous:
- A function is right-continuous at a point if the limit of the function as the variable approaches that point from the right exists and is equal to the function value at that point.
2. Left-Continuous:
- A function is left-continuous at a point if the limit of the function as the variable approaches that point from the left exists and is equal to the function value at that point.
3. Continuity:
- A function is continuous at a point if it is both right-continuous and left-continuous at that point. In other words, the function has no jumps, breaks, or discontinuities at that specific point.
Relationship between Continuity and One-Sided Continuity:
- Continuity requires both right-continuity and left-continuity. A function is continuous at a point only if it behaves smoothly from both the right and the left at that point.
- One-sided continuity refers to the behavior of a function approaching a point either from the right or the left. If a function is continuous at a point, it means that it is continuous from both the right and the left at that point.
