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Finding the domain of a function

Source: licencja: CC 0.

Wyznaczanie dziedziny funkcji

Learning objectives

You will develop the following competences: communicating in English, mathematical, IT and basic scientific and technical competence, your learning skills.

You get to know the method of finding the domain of a function.

You will use the information about a function and its domain in geometry tasks.

Learning effect

  • You will learn to find the domain of a function.

  • You will learn to uses the information about a function and its domain in geometry tasks.

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nagranie abstraktu

Get your knowledge about the functionfunctionfunction in order. Complete the sentences:

  • The functionfunctionfunction 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 …

  • functionfunctionfunction can be described using words, a graph or ….

The aim of the class is finding the domain of a functiondomain of a functiondomain of a function.

Task 1
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nagranie abstraktu

Analyse the material presented in the applet. Observe the relations between the volume of the right square prismright square prismright square prism and the length of its edge of the base. Find the domain of a functiondomain of a functiondomain of a function described in the applet.

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Aplet geogebry - Wyznaczanie dziedziny funkcji. Poniżej znajduje się galeria będąca wersją alternatywną dla aplikacji.
Source: GroMar, licencja: CC BY 3.0.

Use the information to solve the tasks.

Task 2
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nagranie abstraktu

Give the formula and the domain of a functiondomain of a functiondomain of a function, which assigns the altitude x of an equilateral triangle to the perimeter of this triangle.

Task 3
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nagranie abstraktu

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 rhombusrhombusrhombus to its area.

Task 4
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nagranie abstraktu

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.

Task 5
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nagranie abstraktu

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.

Task 6
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nagranie abstraktu

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.

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nagranie abstraktu

Having finished all the tasks think what the common property of all sets being the domains of considered functions is.

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nagranie abstraktu

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

Task 7

An extra task:

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nagranie abstraktu

Sketch a graph of a functionfunctionfunction, 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) and B (3, 0).

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nagranie abstraktu
  • The domain of a functiondomain of a functiondomain of a function describing geometric relations is always a positive subset of the set of real numbers.

Exercises

Exercise 1
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Wersja alternatywna ćwiczenia: Determine which sentence is true. Możliwe odpowiedzi: 1. The perimeter of a rectangle equals 20. The length of one of its sides equals x. The function describing the area of this rectangle is expressed in a formula P(x)=10x-x2. The domain of this function is set D=(0,20)., 2. The area of a right triangle equals 24. One of its legs had length x. The function describing length c of the hypotenuse of this triangle with respect to x. is expressed with formula c(x)=x2+2304x2. The domain of this function is set D=(0,)., 3. The sum of digits in a two-digit number equals 13. The digit of the units is x. Presenting this two-digit number as a function of variable x, we get f(x)=130-9x. The domain of this function is set D={4,5,6,7}.
zadanie
Source: GroMar, licencja: CC BY 3.0.
Exercise 2

The area of the rhombus equals 16. The length of one of its diagonals equals x. Give the formula of the function describing with respect of the length of the side f of this rhombus to x.

Give the domain of this relation.

Exercise 3

Describe in English the domain of the function.

Exercise 4
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Wersja alternatywna ćwiczenia: Indicate which pairs of expressions or words are translated correctly. Możliwe odpowiedzi: 1. dziedzina funkcji - domain of a function, 2. funkcja - function, 3. graniastosłup prawidłowy czworokątny - right square prism, 4. trójkąt prostokątny - right-angled triangle, 5. romb - rectangle, 6. prostokąt - rhombus
zadanie
Source: GroMar, licencja: CC BY 3.0.
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Interaktywna gra, polegająca na łączeniu wyrazów w pary w ciągu jednej minuty. Czas zaczyna upływać wraz z rozpoczęciem gry. Jeden ruch to odkrywanie najpierw jednej potem drugiej karty z wyrazem. Każdy wyraz jest odczytywany. Kolejny ruch to odkrywanie trzeciej i czwartej karty. W ten sposób odsłuchasz wszystkie wyrazy. Nawigacja z poziomu klawiatury za pomocą strzałek, odsłuchiwanie wyrazów enterem lub spacją. Znajdź wszystkie pary wyrazów.
Source: Zespół autorski Politechniki Łódzkiej, licencja: CC BY 3.0.

Glossary

domain of a function
domain of a function

dziedzina funkcji

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wymowa w języku angielskim: domain of the function
function
function

funkcja

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wymowa w języku angielskim: function
rectangle
rectangle

prostokąt

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wymowa w języku angielskim: rectangle
rhombus
rhombus

romb

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wymowa w języku angielskim: rhombus
right square prism
right square prism

graniastosłup prawidłowy czworokątny

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wymowa w języku angielskim: right square prism
right‑angled triangle
right‑angled triangle

trójkąt prostokątny

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wymowa w języku angielskim: right‑angled triangle

Keywords

domain of a functiondomain of a functiondomain of a function

functionfunctionfunction

rhombusrhombusrhombus

right square prismright square prismright square prism

right‑angled triangleright‑angled triangleright‑angled triangle