Functions in JavaScript serve a similar purpose to methods in Java, allowing developers to encapsulate reusable blocks of code. However, JavaScript's function syntax is more straightforward compared to Java's method declarations, which include access modifiers, return types, and exception lists. In JavaScript, functions are defined using the function keyword along with a name and parameter list, omitting the need for explicit return type or access level spceifications.

There are three primary ways to define functions in JavaScript:

1. Standard Function Declaration:

   function functionName(parameters) {
       // function body
   }
   

2. Function Expression Using Variable Assignment:

   var functionName = function(parameters) {
       // function body
   };
   

3. Function Constructor (Less Common):

   var functionName = new Function('parameter1', 'parameter2', 'return parameter1 + parameter2;');
   

Example implementation:

function greet() {
    alert("Hello");
}

var greet2 = function() {
    alert("You're great");
};

var greet3 = new Function('alert("You are amazing");');

greet();
greet2();
greet3();

Function parameters and return values work as follows:

• The number of arguments passed during invocation does not have to match the number of formal parameters defined in the function.
• A function can return a value using the return statement.

Example demonstrating parameter handling and return values:

function displayValues(a, b, c) {
    alert("a:" + a);
    alert("b:" + b);
    alert("c:" + c);
}

// Calling with fewer arguments
// displayValues(1, 2);

// Calling with extra arguments
// displayValues(10, "hello js", false, new Date());

function calculateProduct(x, y) {
    var result = x * y;
    return result;
}

// var product = calculateProduct(10, 20);
// alert(product);

// Passing functions as arguments
function addNumbers(i, j) {
    return i + j;
}

function executeOperation(operation) {
    return operation(10, 20);
}

var total = executeOperation(addNumbers);
alert(total);

In JavaScript, functions are first-class citizens, enabling them to be passed around like variables, used as arguments, or returned from other functions.