Topicm59fbbc1fa9bb4575_1528449000663_0Topic

Reading properties of the function based on its plot

Levelm59fbbc1fa9bb4575_1528449084556_0Level

Third

Core curriculumm59fbbc1fa9bb4575_1528449076687_0Core curriculum

V. Functions. The student:

4) reads from the graph 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 function (if they exist) in the closed interval and arguments for which the function takes greatest and smallest values.

Timingm59fbbc1fa9bb4575_1528449068082_0Timing

45 minutes

General objectivem59fbbc1fa9bb4575_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm59fbbc1fa9bb4575_1528449552113_0Specific objectives

1. Reading properties of the function based on its graph.

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

Learning outcomesm59fbbc1fa9bb4575_1528450430307_0Learning outcomes

The student:

- reads properties of the function based on its graph.

Methodsm59fbbc1fa9bb4575_1528449534267_0Methods

1. Discussion.

2. Thematical contest.

Forms of workm59fbbc1fa9bb4575_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm59fbbc1fa9bb4575_1528450127855_0Introduction

At home, students prepare any graph of a function consisting of four line segments, on a checked piece of paper.

The teacher introduces the subject of the lesson – reading properties of the functionproperties of the functionproperties of the function from the graph.

Procedurem59fbbc1fa9bb4575_1528446435040_0Procedure

Task
Students work individually, using computers. Their task is to read properties of the functionproperties of the functionproperties of the function based on its plot.

[Slideshow]

The teacher announces a thematical contest. Students do the exercises in groups. Each groups gets points for the correct solutions and for the time it took them to do the exercises. The group that gets the most points gets a grade.

Contest task
In the picture there is the plot of the functionplot of the functionplot of the function k.

[Illustration 1]

Calculate:

a) $k\left(\sqrt{3}+2\right)$,

b) the sign of the product $k\left(-3\right)·k\left(2\right)$,

c) the sum of the greatest and the smallest value of the function.

Contest task
Draw a plot of the functionplot of the functionplot of the function whose arguments x meet conditions -2 < x < 7 and:

a) the function has the greatest value equal to 5 for the argument 2,

b) the function has four roots,

c) the function takes negative valuesnegative valuesnegative values for each argument such that 0 ≤ x ≤ 3.

Contest task
There is the plot of the functionplot of the functionplot of the function.

[Illustration 2]

a) Calculate the sum of the greatest and the smallest value of the function f.

b) Give the greatest and the smallest value of the function in the interval 〈-2, 2〉.

Contest task
Describe properties of the function g presented in the picture.m59fbbc1fa9bb4575_1527752263647_0Describe properties of the function g presented in the picture.

[Illustration 3]

The teacher sums up the task contest, clears the doubts and grades the groups’ work.

Students work in pairs. They exchange pieces of paper with the drawn function they prepared at home. They read properties of the functionproperties of the functionproperties of the function presented on the graph. Then, they give back the pieces to each other and check if the solutions are correct. They consult possible problems with the teacher.

An extra task:
Draw the plot of the function f(x) = 2x - 4 and discuss its properties.m59fbbc1fa9bb4575_1527752256679_0An extra task:
Draw the plot of the function f(x) = 2x - 4 and discuss its properties.

Lesson summarym59fbbc1fa9bb4575_1528450119332_0Lesson summary

Students do the revision exercises.

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

Describing properties of the functionproperties of the functionproperties of the function based on its graph is giving:

a) the domaindomaindomain,

b) the rangerangerange,

c) roots of the function,

d) positive and negative valuesnegative valuesnegative values,

e) the greatest and the smallest values of the function (if they exist),

f) the monotonicity intervals.

Selected words and expressions used in the lesson plan

domaindomaindomain

negative valuesnegative valuesnegative values

plot of the functionplot of the functionplot of the function

properties of the functionproperties of the functionproperties of the function

rangerangerange