Reimplementation of a Hashtable and hash function
Your container isn't what most people would call a hash table.  It doesn't use a deterministic hash function of its contents, and it doesn't give the expected performance.  That said, here are some other comments on your "container".

myHashtable.myHashFunction(elements, myHashtable.slots);


This is a strange name for the function that adds elements to your container.

private Object[] slots;
slots = new String[size];
public void myHashFunction(Object[] elements, Object[] slots)


Your class acts like it can work on any Object, but it will fail if given anything other than a String.

Arrays.fill(slots, "-1")


This is a strange string to use as your empty sentinel.  What happens if someone wants to add "-1" to your container?  What's wrong with null as an empty marker?