Hi y'all I was just wondering if anyone could help me out with some examples of the following:

a function f where two of the following conditions hold:

--f is continuous on [a,b],

--the interval [a,b] is closed,

--the interval [a,b] is bounded,

yet f is not bounded on [a,b].

a function f where two of the previous conditions hold and f IS bounded on [a,b].

a function f where $\displaystyle f

\to \mathbb{R}$ with $\displaystyle D\subseteq \mathbb{R}$ closed and bounded which does not attain its maximum value in D.

Thanks in advance for any help!