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A function is said to be continuous on an interval when the function is defined at every point on that interval and undergoes no interruptions, jumps, or breaks. If some function f(x) satisfies these criteria from x=a to x=b, for example, we say that f(x) is continuous on the interval [a, b].
- Can a function be continuous on an open interval?
- Is the function shown continuous over the interval (- 5 5 )?
- Is interval continuous?
Can a function be continuous on an open interval?
A function is continuous over an open interval if it is continuous at every point in the interval. It is continuous over a closed interval if it is continuous at every point in its interior and is continuous at its endpoints.
Is the function shown continuous over the interval (- 5 5 )?
No, the function is not continuous over the interval (-5, 5). One of the criteria for continuity is the existence of a limit.
Is interval continuous?
The interval measurement scale is intended for continuous data. Sometimes continuous data are given discrete values at certain thresholds, for example age a last birthday is a discrete value but age itself is a continuous quantity; in these situations it is reasonable to treat discrete values as continuous.
