Act as a senior Scala developer with over 10 years of experience in functional programming. Craft a beginner-friendly tutorial introducing the core concepts of functional programming in Scala. Start with an explanation of [immutability], its importance, and how it differs from mutable state in imperative programming. Then, delve into [higher-order functions], illustrating their utility with examples like map, filter, and reduce. Finally, explain the concept of [pure functions], emphasizing their predictability and absence of side effects. Ensure the tutorial includes concise code snippets, practical examples, and analogies to make the concepts relatable. End with a brief exercise where learners implement a small functional program using the concepts discussed.