How do debounce and throttle use closures in JavaScript?

Data privacy, memoization, once-utilities, currying, event handlers with state, throttle/debounce, function factories, and iterator-like patterns. Anywhere a function needs to remember variables from where it was defined, closures are used.

The memoize function closes over a cache object. The returned function checks the cache before calling the original function. If the result is cached, it returns immediately. Otherwise, it computes, stores, and returns. The cache is private to the closure.

A factory function takes a configuration parameter and returns a new function that closes over it. For example, multiplier(2) returns a function that always multiplies by 2. Each call to the factory creates a separate closure with its own parameter.