By definition of amplitude, in order for a function to have an amplitude the function must be...

Question

There are 2 possible answers I can choose from. Either Bounded or Continuous

Answer 1

It must be bounded in order to have a finite maximum, which is the amplitude.  Being continuous is not a sufficient condition.

 

Examples:

 

f(x) = e^x 

 

is continuous everywhere, but is not bounded as x→∞.

 

g(x) = 5 sin(x) has a maximum value or amplitude of 5.  It is bounded over the full domain of (-∞,∞).