The second is correct, for the first one, generally works (I assume that's what you meant..)
If we let a and b be real numbers with a < b, what would be an example of a continuous f on [a,b) which is not bounded, and what would be an example of a continuous f on [a, ) which is not bounded?
for the first one would 1/x-1 work? and for the second part would f(x)=x work?