The study features for beginners

function with some area designation called matching, in which each number x with a certain set is assigned a certain number of full y.

usually functions represent Latin letters.Consider the example of any f.The number y, which corresponds to the number of x, called the f value of the particular point in x.Are as: f (x).The domain of the function f - is D (f).The area which consists of all values ​​of the function f (x), where x is an argument domain, called the domain of values ​​of f.It is written as: E (f).

The most common function set using formulas.At the same time, if you do not define additional restrictions, area designation function, which is given by the formula, will be considered as the set of values ​​of a variable, and this formula is the place to be.

union of two sets is called a set, each element of which may belong to and owned by at least one of the data sets.

to denote numbers refer to the field of x is selected some of the letters, which is called the independent variable, or argument.

often considered the areas in which the range of values ​​and area designations are not numerical sets.

When is the study of the function, examples can be seen with the help of graphics.The graph of the function is the set of points on the coordinate plane, where the argument "runs" designate the entire area.In order to coordinate subset of the plane was the schedule of a function, it is necessary that a subset have at least one point in common with any line that is parallel to the x-axis.

function is called on the set of a growing, if the higher value of the argument with so many answers the higher value functions, and descending on the set - a higher value if the argument corresponds to the lower value of the function.

The study features in the rise and descent of the need to designate periods of growth and decline of the maximum length.

function called steam if, for any argument with its region designation to f (-x) = f (x), or unpaired - if, for any argument with the area designation will be f (-x) = - f (x).Besides, the graph function pair is symmetrical about a vertical axis, and a graph unpaired - symmetrical about the point (0, 0).

In order to avoid errors when the functions carried out the study, you must learn to find characteristics.To do this, you must do these steps:

1. Find the area designation.

2. Carry out a check on the pairing or unpaired, as well as the frequency.

3. It is necessary to find a point of the graph of a reticle ordinate and abscissa.

4. At this point, you need to find the intervals where the function is positive, and where - negative.These intervals are called gaps with constant characters.That is, you need to determine where the graph is - above or below the x-axis.

5. greatly facilitate the task of graphing information about at what intervals the function increases and decreases to the public.These intervals are called intervals of growth and gaps the descent.

6. Now you need to find the values ​​of the function at the points where the growth is replaced by descent, or vice versa.

This study makes it possible to build a function graph.In addition, it is necessary to find a point of extreme.What it is?

point will be the minimum point, if, for all values ​​of the argument at some point range just to inequality f (x) & gt; f (x0).

point is the maximum point, if for all values ​​of the argument at some point range just to inequality f (x) & lt; f (x0).The most common chart extrema takes the form of the hump and the minimum point - depression.The points of maximum and minimum - extremum point, and the value of the function at the points - extreme.Investigation of the extremum has a tremendous help in the construction schedule.