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Aplikovaná matematika

Kapilota Funkce v rámci předmětu Aplikovaná matematika zpracovává přehled elementárních funkcí včetně funkcí goniometrických. Vždy je vysvětlena základní funkce, pak jsou uvedeny trasformace této funkce v soustavě souřadnic (posunutí po ose x, po ose y), absolutní hodnota základní funkce, popř. funkcí posunutých. Dále jsou zařazeny příklady na aplikaci základních funkcí tak, aby student měl možnost propojit poznatky získané v matematice s praxí. Materiál je určen pro učitele i pro studenty. Snahou bylo vyrobit materiál tak, aby jej mohl student využívat při studiu i bez hlubší znalosti WM (obměnou parametrů jí nadefinovaných funkcí). Přínos práce je v okamžitém a přesném vykreslení grafu nebo celé soustavy grafů. Usnadní se tak práce učitele i studenta.

1. sada úloh:

Lineární funkce

Graf lineární funkce s absolutní hodnotou

Grafické řešení soustavy dvou lineárních rovnic

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CDF
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DOCX

Grafické řešení soustavy dvou lineárních rovnic: x + y = 1 a 2x + y = 2

Lineární lomená funkce

Kvadratická funkce

2. sada úloh:

Graf kvadratické funkce s absolutní hodnotou

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NB
DOCX

Graf funkce ( kvadratické s absolutní hodnotou ) : y =|x^2- 8|x| + 10|

Mocninná funkce s přirozeným exponentem

Mocninná funkce s celým záporným exponentem

Mocninná funkce - transformace souřadnic, absolutní hodnota

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DOCX
Mocninná funkce - transformace souřadnic, absolutní hodnota
Mocninná funkce - transformace souřadnic, absolutní hodnota

Exponenciální funkce

3. sada úloh:

Grafy exponenciálních funkcí - 1

Grafy exponenciálních funkcí - 2

Logaritmická funkce

Logaritmická funkce - transformace souřadnic, absolutní hodnota

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CDF
NB
DOCX

Vztah mezi logaritmickou a exponenciální funkcí o stejném základu.

Goniometrické funkce - sinus

4. sada úloh:

Goniometrické funkce - kosinus

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NB
DOCX
Goniometrické funkce - kosinus Goniometrické funkce - kosinus

Goniometrické funkce - tangens

Goniometrické funkce - kotangens

Goniometrické funkce - transformace souřadnic

Goniometrické funkce - absolutní hodnota

5. sada úloh:

Aplikace goniometrických funkcí - grafické řešení goniometrické rovnice

Kuželosečky - kružnice

Kuželosečky - elipsa

Kuželosečky - hyperbola

Kuželosečky - parabola

Prostor pro dotazy

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