Basic power a>10 10"> 10"> 10" title="Basics of power and>10"> title="Basic power a>10"> !}!}
The graph of the curve function is called exponent a>10 1 0"> 1 0"> 1 0" title="The graph of the curve function is called an exponential a>1 0"> title="The graph of the curve function is called exponent a>10"> !}!}
The geometrical feature of the graph of the function The Ox axis has a horizontal asymptote of the graph of the function at x -, when a >1 at x -, when a >1 at x +, when 0 1 at x - for a >1 for x +, for 0"> 1 for x -, for a >1 for x +, for 0"> 1 for x -, for a >1 for x +, for 0" title =" Geometrical feature of the graph of the function The Ox axis has a horizontal asymptote of the graph of the function at x -, when a > 1 at x -, when a > 1 at x +, when 0"> title="The geometrical feature of the graph of the function The Ox axis has a horizontal asymptote of the graph of the function at x -, when a >1 at x -, when a >1 at x +, when 0"> !}!}
Showy equals are called equal to the form a>0,a1 and equal to what kind 0,a1, and rivnyannya, which is reduced to this type"> 0,a1, and rivnyannya, which is reduced to this kind"> 0,a1, and rivnyannya, which is reduced to this kind" title="Showing rivnyannya call jealousy of the form a>0, a1, that jealousy that is reduced to this type"> title="Showy equals are called equal to the form a>0,a1 and equal to what kind"> !}!}
The main methods of unraveling display levels Functional-graphic Functional-graphic Based on various graphic illustrations or any other functions. Method of equalization of indicators Method of equalization of indicators Based on the established theorem: Equalization is equal to equalization f(x)=g(x), where a>0,a1. Method of introducing a new change Method of introducing a new change 0, a1. Method of introducing a new change Method of introducing a new change"> 
0,a1, that inequality, which can be reduced to this form. Theorem: Showing unevenness is equal to f(x)>g(x), so a >1 ; Showing unevenness is the same" title=" Showing unevenness Showing unevenness is called unevenness of the form a>0, a1, and unevenness, which is reduced to this type. Theorem: Showing unevenness is equal value of inequality f(x)>g(x), a > 1;" class="link_thumb"> 8 !}!} Show inequalities Show inequalities are called inequalities of the form a>0, a1, and inequalities that can be reduced to this type. Theorem: Showing inequality of previous inequality f(x)>g(x), if a >1; Showing the unevenness of old unevenness f(x) 0,a1, that inequality, which can be reduced to this form. Theorem: Showing inequality of previous inequality f(x)>g(x), if a >1; Display inequality is equal to "> 0,a1, and inequality, which is reduced to this form. Theorem: Display inequality is equivalent to inequality f(x)>g(x), if a>1; ,a1, and inequality, what to call to whom Theorem: Showing unevenness of previous irregularities f(x)>g(x), if a >1 ; Showing unevenness of kind of "title=" Showing of unevenness Showing unevennesses are called inequalities of type a>0 ,a1, and unevenness , which can be reduced to this form. Theorem: Display inequality is equal to inequality f(x)>g(x), a > 1; Display inequality is equal to n"> title="Show inequalities Show inequalities are called inequalities of the form a>0, a1, and inequalities that can be reduced to this type. Theorem: Showing inequality of previous inequality f(x)>g(x), if a >1; Displayed inequality is equally strong"> !}!}
At the hour of teaching 1 lesson on the topic “Display function” with a handbook: Algebra and the beginning of analysis 10-11 - edited by A.G. Mordkovich, it is very easy to correct this presentation, because The hour is approaching for illustrating various authorities and rules, it is possible to quickly verify small s/r, when explaining new material, you can vikorist the initial schedules of the display function.
Fragments of this lesson can be reviewed during the hour of repetition of the material covered and preparation before the test.
Koliorovimi geometric figures the slides show hyper-strength.
To stay ahead of the curve, create your own Google account and go to: https://accounts.google.com
Lesson on the topic "Display function".
Lesson type: lesson on learning new material
Lesson meta: about In order to ensure that students have acquired knowledge about the display function, and power, create the minds for development, be able to extract knowledge for additional activities pre-investigative activity and analysis of the situation.
Get started:computer, classroom, slide presentation, interactive board, handbook “Algebra and the beginnings of analysis 10-11” edited by A.G. Mordkovich, chair tools, cards.
Head to the lesson.
This game is carried out by updating the knowledge of students in the lesson and learning new material on the topic “Display function and graph”.
I learn to respond to power for 60 seconds. (leaflets distributed behind the scenes)
The title of “the most intelligent person in the classroom” is given to those who rely on more nutrition. (Result at the end of the lesson - you can prepare mini-prizes)
Feeding:
(foreign region)
11) What does the letter E mean?(area value)
12) The graph of an unpaired function is symmetrical.
(cob coordinates)
13) What is the language about? Chim less x, the more y. (Spadannya)
14) The impersonality of whole numbers - what kind of letter?(Z)
15) Points of the crossbar of the function graph from all directions Oh (zero functions)
16) There are no active numbers - what kind of letter?(R)
17) Power of function f(-x) = - f(x) (unpaired)
Checking the evidence slide No. 3
a) appointment
Today you have to do a lot of darkness, work on your thoughts, and resist.
In life, we often struggle with differences between values. The assessment based on the control robot depends on the quantity and correctness of the entered orders, the quality of purchase depending on the quantity of purchased goods and prices. Some deposits may be of a temporary nature, others are permanent.
Let's take a look at these laws. Slide 4-6
The growth of the village is subject to the law A=A 0* a kt
A- changing the number of trees per hour;
A 0 - cob quantity of wood;
t-hour, before, a- deeds are permanent.
The pressure continues to change according to the law: P = P 0 * a -kh
P - Vise at height h,
P0 - Press on the level of the sea,
A - Deyaka is calm.
Changing the amount of bacteria N=5 t
N - number of bacterial colonies at time t
T - hour of reproduction
What is more suitable for this process? Slide No. 7- similarity to the form of the formula that sets the law y = c · a kh
The topic of our lesson display function. Slide number 8 (recorded by Zoshitah)
Let us put in these formulas c = 1, k = 1, which function is removed? - y = a x
please check the schedule Slide No. 9
what is this function?
B) practical robot. Slide No. 10
Option 1 Option 2
Create function graphs
Y \u003d 2 x, y \u003d (1/2) x
For a break [-2; 3] with crop 1.
Let's check the correctness of your actions Slide No. 11
Let's adjust the graphs of the function y = 2 x, y = (3/2) x, y = (5/2) x
-What kind of jewels can we earn? -The larger the base, the flatter the schedule.
And now we level the graphs of the function y = (1/2) x, y = (4/6) x, y = (1/3) x and we will create the same symbols. -The greater the base, the flatter the schedule.
These functions are called ostentatious.
And today, in the guilty lesson, the importance of the display function is important, we will look at the actions of power and learn to stand in power during the conquest of the command, a great look.
So try to formulate the meaning of the display function.
(Scholars confirm, dear reader, that it is necessary to correct the meaning).
(On slide No. 12 the meaning appears, learn to write it down in the form)
Add a function to the assigned circuit. Slide No. 13
The skin version continues its function
1. Area of significance of the function.
2. Area of function value.
3. Points of the web with coordinate axes.
4. Intervals of growth and decline.
V ) verification of the results of practical work.
Slide №14,15
Graphs of functions appear on the screen, and they are called power are demonstrated. Learn to take notes from the Zoshits.
4. Fastening of the worn one.
I will preach to you the activities of the lesson on the topic of our lesson.
a) Orally .(students choose the correct substrate, primer and choice)
1." Select display function».
A) Functions from afar are recorded on your device
; ; ; ; ; ; ; ; ; .
b) . From the given list of functions, select the function you want
Like for show: (On slide 16)
The remaining function-solution in the garden Slide No. 17
3. Given the function: y = a x ±b. Give the rule, for what you can,
Not ending every day graphics of this function,
know the range of values of the function. Slide No. 18-19 (rule written down by Zoshit)
Visnovok:
If y = a x + b, then E(y) = (b; +∞)
Yaxcho y = a x -b, then E(y) = (-b; +∞)
4 . Indicate the function that is growing. Slide No. 20
5. Select the decay function.
b) in writing.
Vikorist and power changes or growth
Using the display function, equalize the date of the date with one :№ 1322
Slide No. 21
G ) Independent robot (if you need help from a teacher). Addendum 1
Option No. 1 | Types | Option No. 2 | Types |
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9,8 0 | 3 -2 | |||||
a x > 1 for a… ,x…. | a > 1, x > 0 or 0 A 1.x 0 | How does y = 8 - x change? | So |
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Foreign region | Whatever the number |
|||||
The impersonal value x, for which the value y(x) is assigned, is called... | Foreign region | X -? | ||||
Display function area | The graph y = a will pass through the Yaku point obov'yazkovo x? | (0,1) |
||||
Foreign region y = 2 x +3 | Whatever the number | Impersonal meaningdisplay functions | E(a x) = R + |
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Impersonal meaning y = √х | y≥0 | a > 1, a x 1 > a x 2 Equalize x 1 and x 2 | x 1 >x 2 |
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6 3 6 – 2 | ||||||
Unravel unrest 3 x 4 | Match the numbers to 1 | |||||
Anonymous value of display function | E(a x) = R + | Foreign region | x≥0 |
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3 x = 1, x = … | 1996 0 | |||||
y = a x . when a> 1 function... | growing | I will name the point | Zero function, does not fray |
|||
Chi is growing y=? | neither | Chi is growing | So |
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15 2 |
5. Homework. (On slide No. 22)
6. Pouch fitment. Ratings. (On slide No. 23)
When conducting a lesson on the topic “Display function”, it is easy to understand this presentation, since there is an hour for illustrating various powers and rules, it is possible to easily revise small s/r, when explaining a new concept. The TV show can be enhanced with more basic graphics and display functions .
Fragments of this lesson can also be reviewed when repeating the material covered, during preparation before the test.
Colored geometric figures on the slides show hyper-strength. (Slide No. 11,16)
Under the hour of preparation of this work, materials were awarded with the permission of the work:
Morina S.A. - mathematics teacher MOU ZOSh No. 5 m.Zheleznovodska
The presentation “Display function, power and schedule” provides basic material on these topics. During the presentation, the power of the display function, its behavior in the coordinate system is clearly examined, the applications of unraveling tasks from the various power functions, equalities and inequalities are examined, and important theorems on the topic are discussed. With additional presentation, the teacher can enhance the effectiveness of the math lesson. Since the presentation of the material helps to respect the students before learning, the animation effects help to clearly demonstrate the unraveling of the task. For more Swedish memory to understand, the authorities and the particularities of the decision are seen in color.
The demonstration begins with the application of the display function y = 3 x with various displays - all positive and negative, as a fraction and tens. Function values are calculated up to the skin level. Next, there will be a graph for this function. On slide 2 there is a table filled with coordinates of points to plot the graph of the function y = 3 x. Behind the dots on coordinate plane There will be a regular schedule. Along with the graph there will be similar graphs y = 2x, y = 5x and y = 7x. Skin function is shown in different colors. Such colors have Wikonan graphics with many functions. Obviously, as the stage of the display function increases, the graph becomes steeper and is closer to the ordinate axis. This slide describes the power of the display function. It is noted that the designated area is the number line (-∞;+∞), the function is not paired or unpaired, and for all areas the designated function grows and does not have the greatest or least value. The display function is bordered at the bottom, but not bordered above, without interruption in the designated area and folded down. The value area of the function is between (0;+∞).
Slide 4 shows the further investigation of the function y = (1/3) x. There will be a graph of the function. And this will fill in the coordinates of the points that will be included in the function graph, table. Behind these points there will be a graph on a rectangular coordinate system. I instruct the authorities to describe the functions. It means that the area assigned is the entire numerical value. This function is neither unpaired nor paired, which varies throughout the entire area of significance, and does not have the greatest or least significance. The function y = (1/3) x is bordered at the bottom and not bordered, at the same time the value is continuous, it has a convexity downward. The value area is positive (0;+∞).
On the applied application of the function y = (1/3) x you can see the power of the display function with a positive basis, less than one and clarify the statements about its graphics. On the slide there are 5 presentations of this function: y = (1/a) x de 0 On slide 6 you will see the graphs of the function y = (1/3) x and y = 3 x. It can be seen that these graphs are symmetrical along the ordinate axis. To ensure that the leveling is complete, the graphs are drawn in colors that represent the function formulas. Next, the display function is assigned. On slide 7, the frame shows a value in which it is indicated that a function of the form y = a x, which is more positive than a, not equal to 1, is called display. Next to the next table is the display function with a base greater than 1 and a positive minus 1. It is obvious that practically all power functions are similar, only the function with a base greater than a, growing, and with the basis, mensha 1, mensha. Next you can see the butts being untied. For butt 1 it is necessary to untie the row 3 x =9. The equation is calculated graphically - there will be a graph of the y function = 3 x graph of the y function = 9. The cross point of these graphs is M(2; 9). Obviously, the equation is equal to the value x = 2. Slide 10 describes the solution to the equation 5 x =1/25. Similar to the front butt, the correct alignment is indicated graphically. Demonstrated as a function of graphs y=5 x y=1/25. The crossing point of these graphs is point E(-2;1/25), therefore, the associated level is x=-2. Next we will look at the solution to the imbalance 3 x<27. Решение выполняется графически - определяется точка пересечения графиков у=3 х и у=27. Затем на плоскости координат хорошо видно, при каких значениях аргумента значения функции у=3 х будут меньшими 27 - это промежуток (-∞;3). Аналогично выполняется решение задания, в котором нужно найти множество решений неравенства (1/4) х <16. На координатной плоскости строятся графики функций, соответствующих правой и левой части неравенства и сравниваются значения. Очевидно, что решением неравенства является промежуток (-2;+∞). The following slides present important theorems that counteract the power of the show function. Theorem 1 confirms that if the equality a m = a n is positive, it is also true if m = n. Theorem 2 states that for a positive value of the function y=a x will be greater than 1 for positive x, and less than 1 for negative x. Confirmation is confirmed by the images of the graph of the display function, in which the behavior of the function in different intervals of the value area is visible. Theorem 3 says that for 0 p align="justify"> Further, in order to master the material, the students look at the application of the best instruction with the help of the learned theoretical material. In application 5 it is necessary to graph the function y = 2 · 2 x +3. The principle of graphing a function is demonstrated by transforming the structure into the form y = a x + a + b. The coordinate system will be transferred in parallel to the point (-1; 3) and the graph of the function y = 2 x will be drawn in parallel with this coordinate system. On slide 18 you can see a more graphical solution to the equation 7 x = 8's. There will be a straight line y = 8 x and the graph of the function y = 7 x. The abscis point of the crossbar of the graphs x=1 equals the solutions. The remaining butt describes the distribution of inequality (1/4) x = x+5. There will be graphs of both parts of the unevenness and it will be indicated that each solution has a value of (-1; + ∞), for which the value of the function y = (1/4) x is always less than the value of y = x +5. The presentation “Display function, power and schedule” is recommended to improve the effectiveness of a school mathematics lesson. The thoroughness of the material in the presentation will help achieve the goals of starting the distance lesson. The presentation can be used for independent work by students who have not mastered the topic well enough in class. A mathematics lesson on the topic “Exhibition function”, grade 10 (handbook “Algebra and the beginning of mathematical analysis, grade 10” by S.M. Nikolsky, M.K. Potapov and others) is divided into additional computer technologies. The lesson examines the function and the power of this function and its graph. These authorities will be victorious in the future, with the authorities achieving a logarithmic function, with the highest levels of apparent equalities and inequalities. Lesson type: combinations of computer and interactive board. Computer technologies offer great potential for activating initial activities. The widespread availability of ICT for a large number of objects makes it possible to implement the principle of “learning from treasures”, and then any object has an equal chance of becoming loved by children. The first lesson in the topic: the first lesson in the topic. Method: combinations (verbal-scientific-practical). Meta for the lesson: formulate statements about the display function, the power and graphics. Lesson task: Material for a selection lesson in such a way that it transfers work from students of different categories - from weak students to strong ones. Lesson progress I. Organizational moment (Slide 1-4). Presentation
II. Development of new material (Slide 5-6) Designated display function; The power of the display function; Display function schedule. III. Usno -
consolidation of new knowledge (slide 7-16) 1) Z'yasuvati, chi є growing function (changing) 2) Match: . 3) Equal with one: 4) The little one shows the graphics of the display functions. Spivvіdnesіt graph of the function from the formula. IV. Dynamic pause V. Consolidation and systematization of new knowledge (Slide 16-20) 1) Induce the graph of the function: y=(1/3) x; 2) Unlock the graphic alignment: 3) Stabilization of the display function until the development of applied tasks: “The period of rapid decline of plutonium reaches 140 dB. How much plutonium will you lose after 10 years, since your cob mass is equal to 8 g? VI. Test robot (slide 21) Kozhen learns to draw a card from the assignments - test (Addendum 1) and a table for entering confirmations (Addendum 2). Verified and evaluated (slide 22) VII. Homework (Slide 23-24) No. 4.55 (a, c, c) No. 4.59, No. 4.60 (a, g); No. 4.61 (g, h) Zavdannya (for those who are interested in mathematics): The depth of the atmosphere is p (in centimeters of mercury) depending on the altitude, which is expressed in kilometers. h above the level of the sea is expressed by the formula Calculate what kind of atmospheric pressure there will be on the top of Elbrus, whose height is 5.6 km? VIII. Suitability of pouches Literature
