Can someone explain first-class functions, higher-order functions, and closures in JavaScript?

A first-class function is a function that JavaScript lets you treat like any other value. You can store it in a variable, pass it as an argument, or return it from another function. A higher-order function is a function that accepts another function, returns one, or does both. For example, `array.map(x => x * x)` is higher-order because `map` receives a function. A closure happens when an inner function keeps access to variables from the surrounding function, even after the outer function has finished running.

A useful distinction is that first-class functions describe what JavaScript allows you to do with functions, while higher-order functions describe a function’s behavior. First-class means a function can be handled as data. Higher-order means the function works with other functions. Closures describe how a function remembers variables from the scope where it was created. These aren’t three competing types of functions; one function can fit all three descriptions.

The easiest way to learn these is by writing small exercises rather than memorizing definitions. Try passing callbacks to `map`, `filter`, and `setTimeout`, then write a function that returns another function. For closures, create a counter such as `const counter = () => { let value = 0; return () => ++value; };`. Each returned function remembers its own `value`. Use a debugger and inspect the variables while the functions run. Closures usually take more practice because they depend on scope and variable lifetime.

Here’s one example that combines the ideas: `const makeAdder = amount => number => number + amount;`. `makeAdder` is a higher-order function because it returns another function. The returned function is first-class because it can be stored in a variable: `const addFive = makeAdder(5);`. It is also a closure because it remembers the `amount` value, so `addFive(10)` returns `15`. Try changing the values and logging each step in your browser’s developer tools.