Maintaining your privacy is important to us. For this reason, we have developed a Privacy Policy that describes how we use and store your information. Please review our privacy practices and let us know if you have any questions.
Collection and use of personal information
Personal information refers to data that can be used to identify or contact a specific person.
You may be asked to provide your personal information at any time when you contact us.
Below are some examples of the types of personal information we may collect and how we may use such information.
What personal information do we collect:
- When you submit an application on the site, we may collect various information, including your name, telephone number, address Email etc.
How we use your personal information:
- The personal information we collect allows us to contact you with unique offers, promotions and other events and upcoming events.
- From time to time, we may use your personal information to send important notices and communications.
- We may also use personal information for internal purposes, such as conducting audits, data analysis and various research in order to improve the services we provide and provide you with recommendations regarding our services.
- If you participate in a prize draw, contest or similar promotion, we may use the information you provide to administer such programs.
Disclosure of information to third parties
We do not disclose the information received from you to third parties.
Exceptions:
- If necessary - in accordance with the law, judicial procedure, legal proceedings, and/or based on public requests or requests from government agencies on the territory of the Russian Federation - disclose your personal information. We may also disclose information about you if we determine that such disclosure is necessary or appropriate for security, law enforcement, or other public importance purposes.
- In the event of a reorganization, merger, or sale, we may transfer the personal information we collect to the applicable successor third party.
Protection of personal information
We take precautions - including administrative, technical and physical - to protect your personal information from loss, theft, and misuse, as well as unauthorized access, disclosure, alteration and destruction.
Respecting your privacy at the company level
To ensure that your personal information is secure, we communicate privacy and security standards to our employees and strictly enforce privacy practices.
Russian gymnasium
ABSTRACT
Completed
student of class 10 “F” Burmistrov Sergey
Supervisor
mathematic teacher
Yulina O.A.
Nizhny Novgorod
Function and its properties
Function- variable dependence at from variable x , if each value X matches a single value at .
Variable x- independent variable or argument.
Variable y- dependent variable
Function value- meaning at, corresponding to the specified value X .
The scope of the function is all the values that the independent variable takes.
Function range (set of values) - all the values that the function accepts.
The function is even- if for anyone X f(x)=f(-x)
The function is odd- if for anyone X from the domain of definition of the function the equality f(-x)=-f(x)
Increasing function- if for any x 1 And x 2, such that x 1
<
x 2, the inequality holds f(
x 1
)
Decreasing function- if for any x 1 And x 2, such that x 1 < x 2, the inequality holds f( x 1 )>f( x 2 )
Methods for specifying a function
¨ To define a function, you need to specify a way in which, for each argument value, the corresponding function value can be found. The most common way to specify a function is using a formula at =f(x), Where f(x)- expression with a variable X. In this case, they say that the function is given by a formula or that the function is given analytically.
¨ In practice it is often used tabular way to specify a function. With this method, a table is provided indicating the function values for the argument values available in the table. Examples of table functions are a table of squares and a table of cubes.
Types of functions and their properties
1) Constant function- function given by formula y= b , Where b- some number. The graph of the constant function y=b is a straight line parallel to the abscissa axis and passing through the point (0;b) on the ordinate axis
2) Direct proportionality - function given by formula y= kx , where k¹0. Number k called proportionality factor .
Function properties y=kx :
1. The domain of a function is the set of all real numbers
2. y=kx- odd function
3. When k>0 the function increases, and when k<0 убывает на всей числовой прямой
3)Linear function- function, which is given by the formula y=kx+b, Where k And b - real numbers. If in particular k=0, then we get a constant function y=b; If b=0, then we get direct proportionality y=kx .
Function properties y=kx+b :
1. Domain - the set of all real numbers
2. Function y=kx+b general form, i.e. neither even nor odd.
3. When k>0 the function increases, and when k<0 убывает на всей числовой прямой
The graph of the function is straight .
4)Inverse proportionality- function given by formula y=k /X, where k¹0 Number k called coefficient of inverse proportionality.
Function properties y=k / x:
1. Domain - the set of all real numbers except zero
2. y=k / x - odd function
3. If k>0, then the function decreases on the interval (0;+¥) and on the interval (-¥;0). If k<0, то функция возрастает на промежутке (-¥;0) и на промежутке (0;+¥).
The graph of the function is hyperbola .
5)Function y=x2
Function properties y=x2:
2. y=x2 - even function
3. On the interval the function decreases
The graph of the function is parabola .
6)Function y=x 3
Function properties y=x 3:
1. Domain of definition - the entire number line
2. y=x 3 - odd function
3. The function increases along the entire number line
The graph of the function is cubic parabola
7)Power function with natural exponent - function given by formula y=xn, Where n- natural number. When n=1 we obtain the function y=x, its properties are discussed in paragraph 2. For n=2;3 we obtain the functions y=x 2 ; y=x 3 . Their properties are discussed above.
Let n be an arbitrary even number greater than two: 4,6,8... In this case, the function y=xn has the same properties as the function y=x 2. The graph of the function resembles a parabola y=x 2, only the branches of the graph for |x|>1 rise steeper the larger n, and for |x|<1 тем “теснее прижимаются” к оси Х, чем больше n.
Let n be an arbitrary odd number greater than three: 5,7,9... In this case, the function y=xn has the same properties as the function y=x 3 . The graph of the function resembles a cubic parabola.
8)Power function with a negative integer exponent - function given by formula y=x -n , Where n- natural number. For n=1 we obtain y=1/x; the properties of this function are discussed in paragraph 4.
Let n be an odd number greater than one: 3,5,7... In this case, the function y=x -n has basically the same properties as the function y=1/x.
Let n be an even number, for example n=2.
Function properties y=x -2 :
1. The function is defined for all x¹0
2. y=x -2 - even function
3. The function decreases by (0;+¥) and increases by (-¥;0).
Any functions with even n greater than two have the same properties.
9)Function y= Ö X
Function properties y= Ö X :
1. Domain of definition - ray)