1. A function is a relation where each input has exactly one output. 2. The domain is the set of all possible inputs for the function. 3. The range is the set of all possible outputs the function can produce. 4. The graph of a function visually represents all input-output pairs on the coordinate plane. 5. Key features of functions include intercepts (where the graph crosses axes), extrema (maximum and minimum points), and continuity. 6. Functions can be classified by their behavior, such as linear, quadratic, polynomial, exponential, and more. 7. Important concepts include function composition, inverses, and transformations (shifts, stretches, and reflections). 8. Understanding functions is fundamental for algebra, calculus, and many real-world applications.