Keyword: «function»

The paper considers the definition of convexity (up, down) of the graph of function using the method of tangents, chords and analytical method. The author formulates signs and related methods to study functions for bulge graphics using the second derivative and functions of generalization.

The paper deals with the problems that lead to the concept of a derivative: the tangent to the curve and the instantaneous rate of change of the function. A generalization function is introduced, which is a derivative, but it is determined without using the theory of limits. The method by which the generalization function is defined is called the generalization method.

The article analyses graphing (sketching) of curves given parametrically without full study using derivatives. The graphing is made with the help of auxiliary curves. This approach to graphing allows to use the article in work both with schoolchildren and with first-year students. The authors give examples of curves graphing and variants of tasks for independent work.

The plotting (sketching) of curves defined in polar coordinate system on the plane is studied. Examples of plotting curves defined in polar coordinate system are given. The variants of the tasks for independent work are presented. The material is available to high school students and can be suggested for their acquaintance with the polar coordinate system, as well as for working with students of the first semester.

The study raises an urgent problem - the theory of functional syntax in Russian linguodidactics. The aim of the article is to present a theoretical analysis of functional syntax as a subject of linguistic research in the practice of teaching Russian as a foreign language. The sources on which the functional syntax is based are analyzed, the applied research of Russian pedagogical scientists, developed in the process of practice, as well as the works of foreign authors that are of great importance for domestic functional grammar are examined. It is established that the methodology for teaching and studying Russian syntax involves the creation of a functional grammar (syntax) based on the functional approach «from value to form» (from functions to means), enabling to study linguistic facts in a different content space, which will facilitate the use of speech functions and concepts with the help of which communication and speech intentions of learners of a foreign language are realized.