The definition and properties of the graph: The structure of the course in the school of mathematical analysis

the first time the notion of function, students secondary schools are usually found in the 7th grade, when they approach to the study of algebra course as a separate branch of mathematics.It begins study of functions, generally without the input of complex definitions and terms, which is quite logical.The most important thing in the familiarization stage - to give students an opportunity to general information on elementary examples of the new and never met him earlier mathematical object.

begins with learning the functions of linear dependency graph is a straight line.Students learn mathematical notation according to one variable from each other and understand what the variable in the function is independent and which - dependent.Parallel to this, the students begin to charting on the coordinate plane on which they had previously observed only points.

following function, who are familiar with the students - a direct proportionality.Initially, the course of algebra authors of many benefits distinguish this relationship apart from the linear functions, noting some important properties of functions that are inherent to this dependence.

After reviewing the basic functions of the students are introduced to the generalized concepts that characterize the numerical dependence.First and foremost, it is work with the record y = f (x).Further lessons necessarily dedicated to the practical application of theoretical knowledge, which is regarded as part of the application and determine the nature of any particular properties of the function characterizing a given process.

In 8th grade students for the first time faced with a quadratic equation.After mastering the skills of solving equations of this type of program include the study of quadratic functions and its main characteristics.Students learn not only plotted on the representation of the equation, but also to analyze the image presented, identifying the main features and properties forming its mathematical description.

9th grade algebra course expands students a variety of known functions.With enough considerable theoretical base on mathematical analysis, students are introduced to the inverse proportionality and fractional-linear function, as well as study the differences in the presentation graphics plane equations and functions.In the latter case it focuses on the fact that the graph of the equation may have one argument - the independent variable - some values ​​of the dependent variable.The functional dependence is characterized by one correspondence independent and dependent variables.

in senior school students learn complex functional dependence and learn to build schedules, based not on the table of values ​​"argument - function", and on the properties of the function.This is due to the fact that the behavior of complex functions is quite difficult to predict "offhand" and calculate a specific set of values ​​is quite difficult.Therefore, to determine the behavior of functions describe its main characteristics: domain and the value of the asymptote, the monotony, the points of maximum and minimum, convexity, and so on. D. Particular attention should be paid to such property as parity.Even and odd functions have a special character of behavior: the first characteristic means that the graph of the function is symmetrical about the vertical axis, the second - with respect to the point of origin.

This completes the study of the foundations of mathematical analysis in the course of high school.Further study will be necessary numerical dependencies presented in the course of higher mathematics, as well as the disciplines devoted to the statistical data.Recent often use an element such as a distribution function.