Topicmc43357245d639623_1528449000663_0Topic

The domain and the range of a function

Levelmc43357245d639623_1528449084556_0Level

Third

Core curriculummc43357245d639623_1528449076687_0Core curriculum

V. Functions

Basic level. The student:

1) identifies functions as clear assignment using word description, table, plot, formula (including formula on different sets).

Timingmc43357245d639623_1528449068082_0Timing

45 minutes

General objectivemc43357245d639623_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesmc43357245d639623_1528449552113_0Specific objectives

1. Identifying the domain and the range of a function.

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

Learning outcomesmc43357245d639623_1528450430307_0Learning outcomes

The student:

- identifies the domain and the range of a function.

Methodsmc43357245d639623_1528449534267_0Methods

1. Discussion.

2. Flipped classroom.

Forms of workmc43357245d639623_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmc43357245d639623_1528450127855_0Introduction

Students at home look for the definition of the function and look for the names of sets $X$ and $Y$ from the definition of the function.

Proceduremc43357245d639623_1528446435040_0Procedure

Flipped clasroom method:

The student chosen by the teacher presents obtained information about sets $X$ and $Y$.

Students in groups compare his/hers presentation with their own information. Together they formulate conclusion to remember.

Important:

There is a functionfunctionfunction $f:X\to Y$.

A set $X$ is called the domain of the functiondomain of the functiondomain of the function and its elements are argumentsargumentsarguments of the function.

A set $Y$ is called the codomain 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 $f$ or all argumentsargumentsarguments of the domain is called the range of function $f$.

Students identify the domain and the range of a given function.

Task 1

Identify the domain and the range of the functionrange of the functionrange of the function described by the graph.

[Illustration 1]

Exemplary solution:

Let’s mark $X$ as the set of names of students and $Y$ as the set of number of letters occurring in the given name. 

The domain of function $f$ is the set of names $X$ = {Janek, Ala, Anetka, Krysia, Adam}. It is a set of 5 elements.

The range of function $f$ is the set $Y$ = {3, 4, 5, 6}. It is a set of 4 elements.

Students use shaped abilities in exercises.

Task 2

Identify the domain and he range of the function presented as a graph.mc43357245d639623_1527752256679_0Identify the domain and he range of the function presented as a graph.

[Illustration 2]

Task 3

Decide if the following correspondences is a function. If yes, give its domain and range.
a) Each student has its name assigned.
b) Each natural number has its additive inverse assigned.
c) Each triangle has the sum of its interior angles assigned.mc43357245d639623_1527752263647_0Decide if the following correspondences is a function. If yes, give its domain and range.
a) Each student has its name assigned.
b) Each natural number has its additive inverse assigned.
c) Each triangle has the sum of its interior angles assigned.

Task 4

[Geogebra applet]

Students work individually using computers. Their task is to identify the domain and the range of a function that assigns the length of the side of the square to its area.

Task 5

Identify sets $X$ and $Y$ in such a way that the correspondencecorrespondencecorrespondence $f:X\to Y$ illustrates a functionfunctionfunction.

Use the following data:

a) A set of numbers expressing the area of a rectangle, a set of rectangles,
b) A set of students in the class, a set of eye colours of students in the class,
c) A set of PESEL numbers, a set of people,
d) A set of female names in the class, a set of letters occurring in the given name.

Task 6

There are sets A = {2, 4, 6, 8} and B = {1, 3, 5}. Draw a graph illustrating such a function that:

a) The set A is its domain and the set B is its range,
b) The set B is its domain and the set A is its range.

Is it possible in both cases?

An extra task:

Odczytaj dziedzinę i zbiór wartości funkcji przedstawionej za pomocą grafu.

Read the domain and the range of a function illustrated on this graph.

[Illustration 3]

Lesson summarymc43357245d639623_1528450119332_0Lesson summary

Students do the revision exercises. Then together they sum‑up the classes, by formulating the conclusions to memorise.

There is a function $f:X\to Y$.

A set $X$ is called the domain of the functiondomain of the functiondomain of the function and its elements are argumentsargumentsarguments of the function.

A set $Y$ is called the codomain 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 $f$ or all argumentsargumentsarguments of the domain is called the range of function $f$.

Selected words and expressions used in the lesson plan

correspondencecorrespondencecorrespondence

functionfunctionfunction

domain of the functiondomain of the functiondomain of the function

range of the functionrange of the functionrange of the function

argumentsargumentsarguments

values of the functionvalues of the functionvalues of the function