Topicm7fc6167b34d6e460_1528449000663_0Topic

Methods of representation of functions

Levelm7fc6167b34d6e460_1528449084556_0Level

Third

Core curriculumm7fc6167b34d6e460_1528449076687_0Core curriculum

V. The functions. The student:

1) defines functions as explicit associationassociationassociation with a verbal description, a tabletabletable, a graph, a formula (also with various formulae on various ranges).

Timingm7fc6167b34d6e460_1528449068082_0Timing

45 minutes

General objectivem7fc6167b34d6e460_1528449523725_0General objective

Interpretation and the use of information presented both in a mathematical and popular science texts also using graphs, diagrams and tables.

Specific objectivesm7fc6167b34d6e460_1528449552113_0Specific objectives

1. Communication in English, developing mathematical, IT and basic scientific and technical competence, developing learning skills.

2. Getting to know various methods of representation of functions.

Learning outcomesm7fc6167b34d6e460_1528450430307_0Learning outcomes

The student:

- gets to know various methods of representation of functions.

Methodsm7fc6167b34d6e460_1528449534267_0Methods

1. Problem competition.

2. Situational analysis.

Forms of workm7fc6167b34d6e460_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm7fc6167b34d6e460_1528450127855_0Introduction

Mini problem competition.

Decide which of the given associations is a functionfunctionfunction.

1. Every person in Poland is associated with a personal identification number.
2. Every European country is associated with its present capital city.
3. Every writer is associated with the tile of the novel, he/she has written.
4. Every natural number is associated with its factor.

Answer:
1. Yes.
2. Yes.
3. No.
4. No.

The teacher assesses the students’ answers and explains any doubts.

Procedurem7fc6167b34d6e460_1528446435040_0Procedure

The teacher informs the students that the aim of the class is getting to know various methods of representation of functions.

The students work in groups to find out how a functionfunctionfunction can be described. They formulate hypotheses and conclusions.

Task 1

Analyse the material in the presentation. Formulate your conclusion concerning the methods of representation of functions.

[Slideshow]

The conclusion:

A function can be describes with a formula, a tabletabletable, a diagramdiagramdiagram or a graph.

Task 2

Two sets $X=\left\{2,4,6,8\right\}$ and $Y=\left\{-1,0,1,2\right\}$ are given. Consider various methods of representation of function $f:X\to Y.$

The students work individually to find out if every diagram represents a function and if every graph represents a function. They formulate hypotheses and conclusions.

Task 3

Analyse the material presented in the interactive figures. Justify why not every case of association is a function. Write down an appropriate conclusion.m7fc6167b34d6e460_1527752263647_0Analyse the material presented in the interactive figures. Justify why not every case of association is a function. Write down an appropriate conclusion.

[Interactive illuustration 1]

[Interactive illustration 2]

The conclusion:

Not every diagramdiagramdiagram or graph presents a functionfunctionfunction.

A graph will present a function if every line parallel to OY axis has at most one interception point with the graph.

A diagram presents a function when every element in set X is related to only one element in set Y.

The students use the information to solve the tasks.

Task 4

The function described with this tabletabletable is given. Give the formula of the function and draw its graph.

[Table 1]

Answer: y = 2x.

Task 5

FunctionfunctionFunction $f:x\to -3x$, where $x\in \left\{-2,-1,0,2,4\right\}$ is given. Give a verbal description of this function.

Task 6

A verbal description of function f is given. Write the formula of this function.

Function f associates every real number to its cube decreased by four.

Answer: $f\left(x\right)=x^3-4$, where $x\in R$.

Task 7

Draw the graph of function f, which associates every number in set $x\in \left\{-5,-4,-3,-2,-1,0,1,2,3,4,5\right\}$ to the absolute value of this number increased by 3.

Task 8

Function f associates every number $x\in \left\{1,6,13,22\right\}$ to the square root of the number greater than it by three. Draw the graph of this function and write its formula.m7fc6167b34d6e460_1527752256679_0Function f associates every number $x\in \left\{1,6,13,22\right\}$ to the square root of the number greater than it by three. Draw the graph of this function and write its formula.

Answer: $f\left(x\right)=\sqrt{x+3},x\in \left\{1,6,13,22\right\}$.

Having solved all the tasks, the students present their results. The teacher assesses their work and explains any doubts.

An extra task

Check (doing the calculations) which of points $A(-3,2),B(0,1),C(\sqrt{2},3),D(1,2)$are included in the graph of function $f\left(x\right)=2.$

Answer: points A and D.

Lesson summarym7fc6167b34d6e460_1528450119332_0Lesson summary

The students do the consolidation tasks. They formulate the conclusions that they need to remember.

- A functionfunctionfunction can be describes with a formula, a tabletabletable, a diagramdiagramdiagram or a graph.

- Not every diagram or graph presents a function. A graph will present a function if every line parallel to OY axis has at most one interception point with the graph. A diagram presents a function when every element in set X is related to only one element in set Y.

Selected words and expressions used in the lesson plan

associationassociationassociation

diagramdiagramdiagram

functionfunctionfunction

graph of the functiongraph of the functiongraph of the function

tabletabletable

verbal description of the functionverbal description of the functionverbal description of the function