Topicm73e3299866998f55_1528449000663_0Topic

Values of the function

Levelm73e3299866998f55_1528449084556_0Level

Third

Core curriculumm73e3299866998f55_1528449076687_0Core curriculum

V. Functions. The student:

1) calculates values of a function given by an algebraic formula;

2) reads and interprets values of functions presented as tables, graphs, formulas etc., also while using the same source a few times, or a few sources at once.

Timingm73e3299866998f55_1528449068082_0Timing

45 minutes

General objectivem73e3299866998f55_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm73e3299866998f55_1528449552113_0Specific objectives

1. Reading and calculating values of functions.

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

Learning outcomesm73e3299866998f55_1528450430307_0Learning outcomes

The student:

- reads and calculates values of functions.

Methodsm73e3299866998f55_1528449534267_0Methods

1. Discussion.

2. Thematical contest.

Forms of workm73e3299866998f55_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm73e3299866998f55_1528450127855_0Introduction

The teacher informs students that during this class they will read and calculate values of functionfunctionfunction described by different methods.

Students give examples of ways of describing functions.

Procedurem73e3299866998f55_1528446435040_0Procedure

[Slideshow]

The teacher informs students that during this class they will read and calculate values of functionfunctionfunction described by different methods.

Students give examples of ways of describing functions.

Task 1

The drawing shows the graphgraphgraph of a function $y=f\left(x\right).$

[Illustration 1]

Read from the graphgraphgraph:

a) $f(-2)andf\left(0\right)$

b) $f(-1) -2f\left(6\right)$

c) for which argument $f\left(x\right)=3,$

d) for which argument of the functionfunctionfunction the value is equal to 0.

Students analyse the following example and calculate values of the function in points -3 and 5.

Example:

Function f is defined by the formula $f\left(x\right)=4x-2.$ We calculate the value of the function for $x=2.$
In order to do that we replace x with number 2 and calculate the value of obtained expression:m73e3299866998f55_1527752256679_0Function f is defined by the formula $f\left(x\right)=4x-2.$ We calculate the value of the function for $x=2.$
In order to do that we replace x with number 2 and calculate the value of obtained expression:

$f\left(2\right)=4·2-2=8-2=6.$

Task contest – students work in 4‑5 persons groups. Each group solves the same set of tasks prepared by the teacher. The prize is getting a grade for correct solution of the tasks.m73e3299866998f55_1527752263647_0Task contest – students work in 4‑5 persons groups. Each group solves the same set of tasks prepared by the teacher. The prize is getting a grade for correct solution of the tasks.

Task 2

Provide a set of functionfunctionfunction values: $f\left(x\right)=2x^2-1,$ if its domaindomaindomain is the set $D=\{-2,-1\frac{1}{2},-\frac{1}{2},0,\frac{1}{2},1\frac{1}{2},2\}$
Draw a graphgraphgraph of this function.

Task 3

Give the domaindomaindomain of the functionfunctionfunction described by the formulaformulaformula $f\left(x\right)=-2x+2,$ if
$R=\{-3,-2,-1,0,1,2,3\}.$ Create a tabletabletable and a graphgraphgraph of this function.

Task 4

Function f is described with the formulaformulaformula $f\left(x\right)=x^3-1.$ Calculate:

a) $f\left(1\right)$,

b) $f\left(0\right)+f(-2)$,

c) $2f(-0,5)-3f(-2)$.

An extra task:

Does number 6 belong in the rangerangerange of the functionfunctionfunction $f$, given by the formulaformulaformula $f\left(n\right)=3n-2$ if the domaindomaindomain of the function $f$ are natural numbers?

Lesson summarym73e3299866998f55_1528450119332_0Lesson summary

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

We call the rangerangerange of function the set of elements from the set Y that have been assigned with elements from the set X.

Selected words and expressions used in the lesson plan

formulaformulaformula

tabletabletable

graphgraphgraph

plotplotplot

word descriptionword descriptionword description

functionfunctionfunction

domaindomaindomain

rangerangerange