A(n) _________ is a key word inside a class declaration that establishes a member’s accessibility.

The keyword we are looking for is "access specifier". It is used to establish a member's accessibility within a class declaration.

Access specifiers are crucial in object-oriented programming because they determine the scope and visibility of class members (variables and functions). By specifying the accessibility of class members, you can control which parts of the code can access them directly. This allows you to implement encapsulation, which is one of the fundamental principles of object-oriented programming.

The three common access specifiers in most object-oriented programming languages (such as C++, Java, and C#) are: 1. private: Class members declared as private can only be accessed within the class itself. They are not accessible by external code or derived classes. 2. protected: Class members declared as protected can be accessed within the class itself and by derived classes. They are not accessible by external code. 3. public: Class members declared as public can be accessed from any part of the code, including external code and derived classes.

Let's consider a simple example of a class with different access specifiers in C++: ``` class MyClass { public: int publicVar; void publicFunction() { // Public function implementation } private: int privateVar; void privateFunction() { // Private function implementation } protected: int protectedVar; void protectedFunction() { // Protected function implementation } }; ``` In this example, `publicVar` and `publicFunction()` are accessible from any part of the code. However, `privateVar` and `privateFunction()` can only be accessed within the `MyClass` class, and `protectedVar` and `protectedFunction()` can be accessed within both the `MyClass` class and any class derived from it.