Topicmf41b94ce89c56444_1528449000663_0Topic

Finding the domain of a functiondomain of a functiondomain of a function

Levelmf41b94ce89c56444_1528449084556_0Level

Third

Core curriculummf41b94ce89c56444_1528449076687_0Core curriculum

I. Functions. The student:

1) Determines functions as unequivocal association by means of word description, tables, graphs, formula (also various formulae in various ranges).

Timingmf41b94ce89c56444_1528449068082_0Timing

45 minutes

General objectivemf41b94ce89c56444_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 objectivesmf41b94ce89c56444_1528449552113_0Specific objectives

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

2. Finding the domain of a functiondomain of a functiondomain of a function.

3. Using the information about a functionfunctionfunction and its domain in geometry tasks.

Learning outcomesmf41b94ce89c56444_1528450430307_0Learning outcomes

The student:

- finds the domain of a functiondomain of a functiondomain of a function,

- uses the information about a functionfunctionfunction and its domain in geometry tasks.

Methodsmf41b94ce89c56444_1528449534267_0Methods

1. Incomplete sentences.

2. Situation analysis.

Forms of workmf41b94ce89c56444_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmf41b94ce89c56444_1528450127855_0Introduction

The students use the incomplete sentences technique to get their information about the functionfunctionfunction in order.

The sentences that they complete:

The function is an association in which …

The domain of a functiondomain of a functiondomain of a function is a set of …

A table is one of the methods of describing …

A functionfunctionfunction can be described using words, a graph or …

The teacher verifies students’ answers and explains any doubts.

Proceduremf41b94ce89c56444_1528446435040_0Procedure

The teacher informs the students that the aim of the class is finding the domain of a functiondomain of a functiondomain of a function.

Task
Students work in groups analyzing the material presented in the applet. Their task is to observe the relations between the volume of the right square prismright square prismright square prism and the length of its edge of the base. The students should find the domain of a functiondomain of a functiondomain of a function described in the applet.

[Geogebra applet]

Students work in small groups solving the tasks.

Task
Give the formula and the domain of a functionfunctionfunction, which assigns the altitude x of an equilateral triangle to the perimeter of this triangle.
Answer: $f\left(x\right)=2\sqrt{3}x,D=(0,\infty )$.

Task
The sum of the lengths of the diagonals in a rhombusrhombusrhombus equals 15. Give the formula and the domain of a functiondomain of a functiondomain of a function, which assigns the length x of one of the diagonals of the rhombus to its area.
Answer: $f\left(x\right)=\frac{1}{2}(15x-x^2),D=(0,15)$.

Task
The perimeter of a rectanglerectanglerectangle equals 80. One of the sides of this rectangle had length x. Give the formula of the functionfunctionfunction describing the length of the diagonal of this rectanglerectanglerectangle with respect to x. Give the domain of this function.
Answer: $f\left(x\right)=\sqrt{2x^2-80x+1600},D=(0,40)$.

Task
The right angle with one leg of the x length is inscribed in a circle with a radius 7. Give the formula of the functionfunctionfunction describing the area of this triangle with respect to x. Give the domain of this function.
Answer: $f\left(x\right)=\frac{1}{2}x\sqrt{196-x^2},D=(0,14)$.

Task
In a right square prismright square prismright square prism a lateral edge is longer than the edge of the base by 5. Give the formula and find the domain of a functiondomain of a functiondomain of a function, which assigns the length of the edge of the base to the total surface area of this cuboid.
Answer: $f\left(x\right)=6x^2+20x,D=(0,\infty )$.

Groups of students present the results of their work.

Discussion – what is the common property of all sets being the domains of considered functions?

The conclusion that the students should formulate:

The domain of a function describing geometric relations is always a positive subset of the set of real numbers.mf41b94ce89c56444_1527752263647_0The domain of a function describing geometric relations is always a positive subset of the set of real numbers.

An extra task
Sketch a graph of a function, whose domain D is the sum of the ranges (- 5, - 1) and (1, 7) and its graph has only two common points with the axis Ox A (-3, 0) i B (3, 0).mf41b94ce89c56444_1527752256679_0Sketch a graph of a function, whose domain D is the sum of the ranges (- 5, - 1) and (1, 7) and its graph has only two common points with the axis Ox A (-3, 0) i B (3, 0).

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

Lesson summarymf41b94ce89c56444_1528450119332_0Lesson summary

The students do the consolidation tasks. They work together to summarize the class and formulate the conclusion to be remembered.

The domain of a function describing geometric relations is always a positive subset of the set of real numbers.mf41b94ce89c56444_1527752263647_0The domain of a function describing geometric relations is always a positive subset of the set of real numbers.

Selected words and expressions used in the lesson plan

domain of a functiondomain of a functiondomain of a function

functionfunctionfunction

rectanglerectanglerectangle

rhombusrhombusrhombus

right square prismright square prismright square prism

right‑angled triangleright‑angled triangleright‑angled triangle