Finitely Determined / k-determined

would anyone be able to tell me what a k-determined function is? I have a definition in my book (Saunders Catastrophe Theory) that states it is a function where every function with the same k-jet is of the same type

I believe type means that the function has the same type of critical points, perhaps in differrent places

I was wondering if someone could explain the definition of k-determined in terms of what they know it to mean, so i can try to understand this a little bit better. Thanks :)