8th grade

Teacher: Melnikova T.V.

Lesson objectives:

Equipment:

Computer, interactive whiteboard, handouts.

Presentation for the lesson.

PROGRESS OF THE LESSON

Lesson plan.

Teacher's opening speech.

Repetition of previously studied material.

Learning new material (group work).

Function study. Chart properties.

Discussion of the schedule (front work).

Game of math cards.

Lesson summary.

I. Updating of basic knowledge.

Greeting from the teacher.

Teacher :

The dependence of one variable on another is called a function. So far you have studied the functions y = kx + b; y =k/x, y=x 2. Today we will continue to study functions. In today's lesson you will learn what a graph of a square root function looks like, and learn how to build graphs of square root functions yourself.

Write down the topic of the lesson (slide1).

2. Repetition of the studied material.

1. What are the names of the functions specified by the formulas:

a) y=2x+3; b) y=5/x; c) y = -1/2x+4; d) y=2x; e) y = -6/x f) y = x 2?

2. What is their graph? How is it located? Indicate the domain of definition and domain of value of each of these functions ( in Fig. graphs of functions given by these formulas are shown; for each function, indicate its type) (slide2).

3. What is the graph of each function, how are these graphs constructed?

(Slide 3, schematic graphs of functions are constructed).

3. Studying new material.

Teacher:

So today we are studying the function
and her schedule.

We know that the graph of the function y=x2 is a parabola. What will be the graph of the function y=x2 if we take only x ≥ 0 ? Part of the parabola is its right branch. Let us now plot the function
.

Let us repeat the algorithm for constructing graphs of functions ( slide 4, with algorithm)

Question : Looking at the analytical notation of the function, do you think we can say what values X acceptable? (Yes, x≥0). Since the expression
makes sense for all x greater than or equal to 0.

Teacher: In natural phenomena and human activity, dependencies between two quantities are often encountered. How can this relationship be represented by a graph? ( group work)

The class is divided into groups. Each group receives a task: build a graph of the function
on graph paper, performing all points of the algorithm. Then a representative from each group comes out and shows the group's work. (Slad 5 opens, a check is carried out, then the schedule is built in notebooks)

4. Study of the function (work in groups continues)

Teacher:

find the domain of the function;

find the range of the function;

determine the intervals of decrease (increase) of the function;

y>0, y<0.

Write down the results for you (slide 6).

Teacher: Let's analyze the graph. The graph of a function is a branch of a parabola.

Question : Tell me, have you seen this graph somewhere before?

Look at the graph and tell me if it intersects the line OX? (No) OU? (No). Look at the graph and tell me whether the graph has a center of symmetry? Axis of symmetry?

Let's summarize:

Now let’s see how we learned a new topic and repeated the material we covered. A game of mathematical cards. (rules of the game: each group of 5 people is offered a set of cards (25 cards). Each player receives 5 cards with questions written on them. The first student gives one of the cards to the second student, who must answer the question from the card . If the student answers the question, then the card is broken, if not, then the student takes the card for himself and passes the move, etc., for a total of 5 moves. If the student has no cards left, then the score is -5, 1 card remains – score 4, 2 cards – score 3, 3 cards – score 2)

5. Lesson summary.(students are graded on checklists)

Homework assignment.

Study paragraph 8.

Solve No. 172, No. 179, No. 183.

Prepare reports on the topic “Application of functions in various fields of science and literature.”

Reflection.

Show your mood with pictures on your desk.

Today's lesson

I liked it.

I didn't like it.

Lesson material I ( understood, did not understand).

Municipal educational institution

secondary school No. 1

Art. Bryukhovetskaya

municipal formation Bryukhovetsky district

Math teacher

Guchenko Angela Viktorovna

2014

Function y =
, its properties and graph

Lesson type: learning new material

Lesson objectives:

Problems solved in the lesson:

teach students to work independently;

make assumptions and guesses;

be able to generalize the factors being studied.

Equipment: board, chalk, multimedia projector, handouts

Timing of the lesson.

Determining the topic of the lesson together with students -1min.

Determining the goals and objectives of the lesson together with students -1min.

Updating knowledge (frontal survey) –3min.

Oral work -3min.

Explanation of new material based on creating problem situations -7min.

Fizminutka –2min.

Plotting a graph together with the class, drawing up the construction in notebooks and determining the properties of a function, working with a textbook -10min.

Consolidating acquired knowledge and practicing graph transformation skills –9min .

Summing up the lesson, providing feedback -3min.

Homework -1min.

Total 40 minutes.

Progress of the lesson.

Determining the topic of the lesson together with students (1 min).

The topic of the lesson is determined by students using guiding questions:

function- work performed by an organ, the organism as a whole.

function- possibility, option, skill of a program or device.

function- duty, range of activities.

function character in a literary work.

function- type of subroutine in computer science

function in mathematics - the law of dependence of one quantity on another.

Determining the goals and objectives of the lesson together with students (1 min).

The teacher, with the help of students, formulates and pronounces the goals and objectives of this lesson.

Updating knowledge (frontal survey – 3 min).

Oral work – 3 min.

Frontal work.

(A and B belong, C does not)

Explanation of new material (based on creating problem situations – 7 min).

Problem situation: describe the properties of an unknown function.

Divide the class into teams of 4-5 people, distribute forms for answering the questions asked.

Form No. 1

y=0, with x=?

The scope of the function.

Set of function values.

One of the team representatives answers each question, the rest of the teams vote “for” or “against” with signal cards and, if necessary, complement the answers of their classmates.

Together with the class, draw a conclusion about the domain of definition, the set of values, and the zeros of the function y=.

Problem situation : try to build a graph of an unknown function (there is a discussion in teams, searching for a solution).

The teacher recalls the algorithm for constructing function graphs. Students in teams try to depict the graph of the function y= on forms, then exchange forms with each other for self- and mutual testing.

Fizminutka (Clowning)

Constructing a graph together with the class with the design in notebooks – 10 min.

After a general discussion, the task of constructing a graph of the function y= is completed individually by each student in a notebook. At this time, the teacher provides differentiated assistance to students. After students complete the task, the graph of the function is shown on the board and students are asked to answer the following questions:

Conclusion: Together with the students, draw a conclusion about the properties of the function and read them from the textbook:

Consolidating acquired knowledge and practicing graph transformation skills – 9 min.

Students work on their card (according to the options), then change and check each other. Afterwards, graphs are shown on the board, and students evaluate their work by comparing it with the board.

Card No. 1

Card No. 2

Conclusion: about graph transformations

1) parallel transfer along the op-amp axis

2) shift along the OX axis.

9. Summing up the lesson, providing feedback – 3 min.

SLIDES – insert missing words

The domain of definition of this function, all numbers except ...(negative).

The graph of the function is located in... (I) quarters.

When the argument x = 0, the value... (functions) y = ... (0).

The greatest value of the function... (does not exist) smallest value - …(equals 0)

10. Homework (with comments – 1 min).

According to the textbook- §13

According to the problem book– No. 13.3, No. 74 (repetition of incomplete quadratic equations)

Consider the function y=√x. The graph of this function is shown in the figure below.

Graph of the function y=√x

As you can see, the graph resembles a rotated parabola, or rather one of its branches. We get a branch of the parabola x=y^2. It is clear from the figure that the graph touches the Oy axis only once, at the point with coordinates (0;0).
Now it is worth noting the main properties of this function.

Properties of the function y=√x

1. The domain of definition of a function is a ray)