Endpoints
Definition
Endpoints are the points that mark the boundaries of an interval on a number line or graph. They can be either included in the interval (closed) or excluded (open).
5 Must Know Facts For Your Next Test
- Endpoints are represented as $(a, b)$ for open intervals and $[a, b]$ for closed intervals.
- In calculus, endpoints are crucial when evaluating limits and continuity at the boundary of a function's domain.
- Endpoints can be found by setting the variable equal to the bounds of the interval.
- For piecewise functions, endpoints determine where each piece of the function starts and ends.
- A function's behavior at its endpoints can significantly affect its overall properties, such as being bounded or unbounded.
Review Questions
- What is the difference between open and closed endpoints?
- How do you determine if an endpoint is included in an interval?
- Why are endpoints important in evaluating limits?
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Related terms
Interval: A set of real numbers that includes all numbers between any two numbers in the set.
Limit: The value that a function approaches as the input approaches some value.
Piecewise Function: A function defined by multiple sub-functions, each applying to a certain interval of the main function's domain.
