Keyword: «modulus»

The article contains a brief presentation of theoretical information in the field of functional dependence of elementary functions. Practical methods that allow you to draw sketches of functions’ curves of different complexity levels are demonstrated here. In particular, the plotting of functions’curves containing modulus usually causes considerable difficulties for university entrants and first-year students. The purpose of this work is to give algorithm for plotting curves of functions containing moduli to which linear transformations are applied. The main attention is paid to the methods of plotting, and not to the study of certain types of functions.

The article presents the problem of mental activity basic techniques using at the mathematics lessons. With their help it is possible to achieve maximum efficiency of learning process through classification and systematization, analyses and synthesis. The authors give examples of the tasks with parameter and illustrate some features of educational activities.

The article proposes a method of presenting the topic “Constructing graphs of multivalued linear functions containing a modulus sign” in the course “Mathematical Analysis”. A brief theoretical information in the field of functional dependence of multivalued linear functions is given. The authors demonstrate practical methods to build the sketches of functions graphs with different levels of complexity. The purpose of this work is to give an algorithm for constructing graphs of multivalued functions, containing a modulus sign, to which linear transformations are applied. The content of the article will be useful for students, as well as for teachers working with the first-year students.

The task of results graphical presentation is sometimes complicated, because it does not always lead to the construction of a graph, which can be quickly depicted on a plane with high quality. The article proposes one of the methods for constructing graphs of multi-valued linear functions containing the modulus sign, namely, the method of splitting the coordinate plane into several areas. Brief theoretical information in the field of functional dependence of multi-valued linear functions is given. The authors demonstrate practical techniques that allow constructing sketches of functions graphs of various complexity levels by the method of plane splitting. The purpose of this work is to give an algorithm for constructing graphs of multivalued functions containing the modulus sign; to show the effectiveness and easiness of constructing graphs using the specified method. The content of the article will be useful to students, as well as to teachers working with the first-year students.

Free knowledge of charting techniques often helps to solve complex problems, and sometimes is the only way to solve them. In the article, the authors propose one of the methods for constructing curves of multivalued linear functions containing the modulus sign, namely, the method of splitting a function into separate equations. Brief theoretical information is given in the field of the functional dependence of multivalued functions. Practical methods of constructing curves of various complexity levels by the method of splitting a function into individual equations are demonstrated. The aim of the work is to systematize and deepen the knowledge of students, to give an algorithm for constructing curves of multivalued functions by methods and techniques that go beyond the school textbook of mathematics. The content of the article will be useful for students, as well as for teachers working with first-year students.