The set of a function values: methodological and calculation aspects

The study of elementary functions is one of the main thematic lines of the pre-university mathematics course. At the same time, the concept of function and related concepts (domain, set of values, graph) represent the most difficult concepts for students. The paper presents the analysis of the formation for the concept of the set of function values and synthesizes its determination methods for different functions. Examples of the use for the set of function values will be useful both for understanding and expanding the concept, and for developing the mathematical capabilities of gifted students.