Double product formula. Formulas of powers and roots

Let's imagine the following situation: you turn on the TV, press the button where there was always 2x2 before, and... You understand that 2x2 has disappeared. The main thing is not to panic. This is temporary and very easy to treat.

If you did not find 2x2 on the usual button, this does not mean that we are gone forever. This means that we have moved to another button. All you need to do is just reset the TV. Then The Simpsons, Family Guy, Rick and Morty, SpongeBob and Avatar marathons will return to your life.

If you are an AKADO subscriber in Moscow

We raise victorious cups and launch fireworks into the sky: thanks to numerous requests from subscribers, 2x2 is returning to the main Akado packages. From November 1, 2017, the TV channel will again be available both in open digital (FTA mode) and in analog format (package "AKADO Antenna" on button No. 37). Thanks to everyone who was worried. We are together again! So let's win!

If you are a ROSTELECOM subscriber in St. Petersburg

Since September 4, 2x2 has changed its broadcasting in the networks of PJSC Rostelecom. The TV channel is no longer on the analog network, but it is available to subscribers of digital and interactive TV - advanced technology for advanced us.

Textbook:

• Makarychev Yu. N., Mindyuk N. R. Mathematics. 7th grade

Goals:

develop graphic literacy charting,

form a habit research work,

to cultivate clarity in the answer, accuracy, responsibility.

I. Student survey

1. What is called a function?

(A function is a dependence of one variable on another, in which each value of the independent variable corresponds to a single value of the dependent variable)

2. What is the scope of a function?

(All the values ​​that the independent variable (argument) takes form the scope of the function)

3. What is the scope of a function?

(All values ​​that the dependent variable takes are called function values)

4. What features are we familiar with?

a) with a linear function of the form y = kx + b,

direct proportionality of the species y = kx

b) with functions of the form y \u003d x 2, y \u003d x 3

5. What is a Linear Function Graph? ( straight). How many points are needed to build this graph?

Without performing construction, determine the relative position of the function graphs given by the following formulas:

a ) y = 3x + 2; y \u003d 1.2x + 5;

b) y \u003d 1.5x + 4; y \u003d -0.2x + 4; y = x + 4;

with) y = 2x + 5; y \u003d 2x - 7; y = 2x

Picture 1

The figure shows graphs of linear functions ( each student is given a sheet with constructed graphs on the desk). Write a formula for each chart

What function graphs are we familiar with? ( y \u003d x 2; y = x 3 )

1. What is a graph of a function y = x 2 (parabola).
2. How many points do we need to build to draw a parabola? ( 7, one of which is the vertex of the parabola).

Let's build a parabola given by the formula y = x 2

x	-3	-2	-1	0	1	2	3
y = x 2	9	4	1	0	1	4	9
y = x 2 + 2	11	6	3	2	3	6	11

Figure 2

What are the properties of a graph of a function y = x 3 ?

1. If a x = 0 , then y = 0 - vertex of the parabola (0;0)
2. Domain: X - any number, D (y) = (- ?; ?) D (y) = R
3. Range of values at ? 0
4. E (y) =
5. The function increases on the interval

   The function increases on the interval )