Topicmaa1fea7eef5ce488_1528449000663_0Topic

Definition of the functionfunctionfunction. Ways of describing the function

Levelmaa1fea7eef5ce488_1528449084556_0Level

Third

Core curriculummaa1fea7eef5ce488_1528449076687_0Core curriculum

V. Functions. The student:

3) reads and interprets values of functions determined by tables, graphs, formulas etc., also in cases of using the same source of information a few times or a few sources at once.

Timingmaa1fea7eef5ce488_1528449068082_0Timing

45 minutes

General objectivemaa1fea7eef5ce488_1528449523725_0General objective

Using mathematical objects and operating them, interpreting mathematical concepts.

Specific objectivesmaa1fea7eef5ce488_1528449552113_0Specific objectives

1. Revising the definition of the function.

2. Describing the function with different ways.

3. Communicating in English, developing basic mathematical, computer and scientific competences, developing learning skills.

Learning outcomesmaa1fea7eef5ce488_1528450430307_0Learning outcomes

The student:

- defines the concept of the function,

- describes the functionfunctionfunction with different ways.

Methodsmaa1fea7eef5ce488_1528449534267_0Methods

1. Discussion.

2. Idea rug.

Forms of workmaa1fea7eef5ce488_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmaa1fea7eef5ce488_1528450127855_0Introduction

The teacher introduces the subject of the lesson – revision of the definition of the function and describing function with various ways.

Proceduremaa1fea7eef5ce488_1528446435040_0Procedure

Students revise the definition of the functionfunctionfunction.

Definition of function

- Function $f$ from the set $X$ into set $Y$ is called correspondence in which each element of the set $X$ corresponds to exactly one element of the set $Y$.

Important:
- There is a function $f:X\to Y$.
- A set $X$ is called the domain of the function and its elements are arguments of the function.
- A set $Y$ is called the range of the function. Each element y of this set which is assigned to at least one argument $x$ of the set $X$ is called the value of function $f$ for argument $x$, which can be written down as $y=f\left(x\right)$.maa1fea7eef5ce488_1527752263647_0Important:
- There is a function $f:X\to Y$.
- A set $X$ is called the domain of the function and its elements are arguments of the function.
- A set $Y$ is called the range of the function. Each element y of this set which is assigned to at least one argument $x$ of the set $X$ is called the value of function $f$ for argument $x$, which can be written down as $y=f\left(x\right)$.
- A set consisting of all elements that are values of function f for all arguments of the domain is called the range of function f.maa1fea7eef5ce488_1527712094602_0- A set consisting of all elements that are values of function f for all arguments of the domain is called the range of function f.

Task
Students work in 5 groups using the rug idea method. The teacher gives each group a piece of paper with the same functionfunctionfunction described in different ways. The students’ task is to describe this function in at least three different ways. They write the propositions of the solutions in the ‘rug’ and present it to other groups.

[Slideshow]

Students analyse the conditions that need to be met so that the graphgraphgraph illustrates a function.

To sum up this part of the class, students decide on the most often used ways of describing the function.

Students use shaped abilities in the exercises.

Task
Give two examples of functions, each defined in the set X = {2, 4, 6, 8} and having the values set Y = {-2, 0, 2}. Describe each one of these functions in 5 ways.

Task
Draw a graphgraphgraph and a plotplotplot of such correspondence from the set X = {2, 4, 6, 8} with set Y = {-2, 0, 2}, that is not a function.

Task
Depending on the length of the side of an equilateral triangle, give formulaformulaformula for the function describing:

a) the perimeter of the triangle,

b) the area of the triangle,

c) the altitude of the triangle.

Task
FunctionfunctionFunction k assigned to each two‑digit number the product of its tens and units digits:

a) calculate k(29),

b) draw a graphgraphgraph and a tabletabletable of this function for arguments that are even numbers, greater than 89.

An extra task:
Function f assigns to each two‑digit number greater than 20 and smaller than 30 the number of its natural divisors. Present the function using a table and a plot.maa1fea7eef5ce488_1527752256679_0An extra task:
Function f assigns to each two‑digit number greater than 20 and smaller than 30 the number of its natural divisors. Present the function using a table and a plot.

Lesson summarymaa1fea7eef5ce488_1528450119332_0Lesson summary

Students do the revision exercises.

Then together they sum‑up the classes, by formulating the conclusions to memorise.

Definition of functionfunctionfunction

- Function $f$ from the set $X$ into set $Y$ is called correspondence in which each element of the set $X$ corresponds to exactly one element of the set $Y$.

- There is a function $f:X\to Y$.

- A set $X$ is called the domaindomaindomain of the function and its elements are arguments of the function.

- A set $Y$ is called the rangerangerange of the function. Each element y of this set which is assigned to at least one argument $x$ of the set $X$ is called the value of functionfunctionfunction $f$ for argument $x$, which can be written down as $y=f\left(x\right)$.

- A set consisting of all elements that are values of function $f$ for all arguments of the domain is called the rangerangerange of function $f$.

Selected words and expressions used in the lesson plan

formulaformulaformula

tabletabletable

plotplotplot

graphgraphgraph

word descriptionword descriptionword description

functionfunctionfunction

domaindomaindomain

rangerangerange