Topicmf134fe5420a16c55_1528449000663_0Topic

Roots of the function

Levelmf134fe5420a16c55_1528449084556_0Level

Third

Core curriculummf134fe5420a16c55_1528449076687_0Core curriculum

V. Functions. The student:

1) reads from the plot of the functionplot of the functionplot of the function: the domain, the range, roots, monotonic intervals, intervals in which the function takes values not greater (not smaller) or smaller (not greater) than a given number, greatest and smallest values of the functionvalues of the functionvalues of the function (if they exist) in the closed interval and arguments for which the function takes greatest and smallest values.

Timingmf134fe5420a16c55_1528449068082_0Timing

45 minutes

General objectivemf134fe5420a16c55_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesmf134fe5420a16c55_1528449552113_0Specific objectives

1. Reading from the plot and calculating roots of the functionfunctionfunction.

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

Learning outcomesmf134fe5420a16c55_1528450430307_0Learning outcomes

The student:

- reads from the plot and calculates roots of the function.

Methodsmf134fe5420a16c55_1528449534267_0Methods

1. Discussion.

2. Situational analysis.

Forms of workmf134fe5420a16c55_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmf134fe5420a16c55_1528450127855_0Introduction

The teacher introduces the subject of the class – reading from the plot and calculating roots of the function.

Proceduremf134fe5420a16c55_1528446435040_0Procedure

Task
Students work individually, using computers. Their task is to read the coordinates of points of intersection of the plot of the functionfunctionfunction and axis X. In particular the first coordinate of each point, that is the zero of the function (the root of the function).

[Geogebra applet]

Based on the analysis of the applet, students define the root of the function.

Definition of the zero of the function:
A zero of the function is each argument for which the function takes the value equal to 0.mf134fe5420a16c55_1527752263647_0A zero of the function is each argument for which the function takes the value equal to 0.

Students use obtained information in exercises.

Task

Read roots of the function presented in the plot.

[Illustration 1]

Task

Check which number is the root of the functionfunctionfunction.

a) y = x - 4; -4, 1, 4

b) y = 2xIndeks górny 3³ + 2; -1, 0, 1

c) y = xIndeks górny 2² - 4; -1, 0, 2

Task

The graphgraphgraph describes the function f. How many roots does this function have? Choose numbers that are roots of the function f.

[Illustration 2]

Task

The plot of the function is made of points of coordinates: (-4;2), (0;3), (9;0), (-1;0), (7;3), (4;0). Does this function have roots? Write them down.mf134fe5420a16c55_1527752256679_0The plot of the function is made of points of coordinates: (-4;2), (0;3), (9;0), (-1;0), (7;3), (4;0). Does this function have roots? Write them down.

Task

Calculate m knowing that number 5 is the root of the function y = (2m + 3)x - 1.

An extra task:

Make a table and plot of a functionfunctionfunction whose domain is a set consisting of 5 elements. Function has exactly three roots, which are negative numbers. Its range are only non‑negative numbers.

Lesson summarymf134fe5420a16c55_1528450119332_0Lesson summary

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

A zero of the functionfunctionfunction is each argumentargumentargument for which the function takes the value equal to 0.

Selected words and expressions used in the lesson plan

zero (root) of the functionzero (root) of the functionzero (root) of the function

values of the functionvalues of the functionvalues of the function

functionfunctionfunction

plot of the functionplot of the functionplot of the function

graphgraphgraph

argumentargumentargument

formulaformulaformula