Standard assumptions on the form of the function F(.) is that it is increasing in K, L, A (if you increase productivity or you increase the number of factors used you get more output) and that it is homogeneous of degree one, or in other words that there are constant returns to scale (which means that if you double both K and L you get double the output). The assumption of constant returns to scale facilitates the assumption of perfect competition which in turn implies that factors get their marginal products: