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

1. Endpoints are represented as $(a, b)$ for open intervals and $[a, b]$ for closed intervals.
2. In calculus, endpoints are crucial when evaluating limits and continuity at the boundary of a function's domain.
3. Endpoints can be found by setting the variable equal to the bounds of the interval.
4. For piecewise functions, endpoints determine where each piece of the function starts and ends.
5. 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?

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.