I am trying to construct/find a multivariate function that can be approximated by a linear function in a specific range of the variable ( I mean a wide ragne and not just a small nbhd) . In this case,when studying the sensitivity of this function in the defined range, only first order sensitivty indexes should be taken in consideration. I would say a function as $$f(x,y)=x+\sqrt{y}+ \cos(x)$$ is good, however such function has no physical meaning.
Can some one help me propsing some well known quasi linear functions or a function that arises from a physics problem ( for example ) in which it can be approximated linearly.
Thank you in advance.