Consider the following functions defined on piecewise domains:

j-x, x<0 iz 2

+ l, x< 0 fl{x) = W, *>0'

h{x) = Ì3X, *>0 '

h{x)~-

3 2 In other cases, one should define an integral by considering the value of the function at the beginning of each time bucket. A notable case occurs in financial engineering models, where the so-called Ito stochastic integral is extensively used. In fact, there are many kinds of integrals, but this is way beyond the scope of this book. See, e.g., Ref. [2] for an elementary introduction to such models.

For each function, indicate whether it is continuous and differentiable at the point of transition between each portion of the domain.