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A mutator function is a function that modifies the state or data of an object. It is typically used to set the value of a private variable within the object or modify its data members in some way. In object-oriented programming, mutator functions are designed to manage and control how data is changed within a class or object, which helps maintain appropriate encapsulation and data integrity. For example, in a class representing a person, a mutator function might be used to set the person's age: ```cpp class Person { private: int age; public: void setAge(int newAge) { // This is a mutator function if (newAge >= 0) { age = newAge; } } }; ``` From the example above, we can see that the `setAge` function is a mutator function as it allows the modification of the person's age while adhering to the class's rules, in this case, ensuring that the age is not negative.

An accessor function is a function that retrieves or "accesses" the state or data of an object, without making any modifications. These functions are typically used to read or get the values of private variables within an object. In object-oriented programming, accessor functions are useful for maintaining encapsulation, as they provide a way for external code to access certain data members of a class without directly modifying the class's internal state or data. For example, in the same class representing a person, an accessor function might be used to get the person's age: ```cpp class Person { private: int age; public: int getAge() const { // This is an accessor function return age; } }; ``` In the example above, the `getAge` function is an accessor function as it provides access to the person's age without making any modifications to the object's state. The `const` keyword ensures that no modifications can be made to the object within this function.