No. A function can be bounded on [a,b] but discontinuous on [a,b]. Here's an example:
Does a function f that is continuous on an open interval (a,b) need to be bounded on that interval?
No. Here's an example:
Does a function f that is discontinuous on a closed interval [a,b] need to be bounded on that interval?
Let . For each given function and interval, determine if we can use the Boundedness Theorem to conclude the function is bounded on that interval. If not, explain why not.
Make it rain.