1) Do member functions occupy space in objects?
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Only if they are virtual.

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when you compile a program, a "symbol table" is created that has information for each datatype used in the program, including basic types. (int, char ...) the information for global functions and member functions of classes is also stored in the same table for later use.

functions are part of the class not the variable. same thing with static members of the class except for one difference. static members can be accessed without actually creating an object but non-static functions have to be called using concrete objects.

so the answer is NO.
yes, and only if they are virtual.
The answer is not simple, because the question is not simple.
There is no consensus on objects implementation in C++, just common aspects and more or less differences between various compilers. However, we can consider that intimate details of relevance for C++ programmers are common to the most implementations, and the differences are important just for the restraint circles of compiler developers. (Compiler development is a quite definite specialty in programing).
The code of a member function  appears just in a single place in a program, related to the class object (the object which is employed by the program as a template for creating instance objects of the class). Each instance object has access to the same piece of code, and the this pointer has some importance in this mechanism. It is suggested a very limited space expense for each instance object, regardless of the number of member functions.
For virtual member functions there is also no code duplication at all. There is a virtual methods table (VMT or vtable) within the class objects, and every instance object has just a special pointer (vpointer) to the virtual methods table.

Good luck !
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