State two types of functions that you know that do not have a maximum or a minimum (unless the domain is restricted to some interval)
How to do this?
When a function is monotonic increasing or decreasing on the domain, such as (-&infin,+∞), it will not have a maximum nor a minimum.
Examples of such functions are
y=x
y=x³
y=e^x
but not y=x², since it is decreasing from (-∞,0], and increasing from [0,+∞), so there is a minimum at x=0.
Some other examples where the limits are not (-&infin,+∞) are:
y=log(x),
y=sqrt(x)
I do not know if I have included all the types, but it would be a good start.