Änderungen von Dokument BPE 2.1 Funktionstypen und deren Eigenschaften

Zuletzt geändert von Holger Engels am 2025/03/31 21:42

Von 2.1 nach 1.1 Von 40.1 nach 39.1

Von Version 39.1

bearbeitet von Holger Engels
am 2024/10/14 12:10

Änderungskommentar: Neues Bild Stetigkeit ei.svg hochladen

Auf Version 2.1

bearbeitet von holger
am 2022/11/13 17:52

Änderungskommentar: Es gibt keinen Kommentar für diese Version

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Zusammenfassung

Seiteneigenschaften (4 geändert, 0 hinzugefügt, 0 gelöscht)
Anhänge (0 geändert, 0 hinzugefügt, 8 gelöscht)

Details

Seiteneigenschaften

Titel

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--BPE 2.1 Funktionstypen und deren Eigenschaften
++Funktionstypen und deren Eigenschaften

Übergeordnete Seite

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--Eingangsklasse.WebHome
++Main.WebHome

Dokument-Autor

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--XWiki.holgerengels
++XWiki.holger

Inhalt

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--{{seiteninhalt/}}
++{{box cssClass="floatinginfobox" title="**Contents**"}}
++{{toc start=2 depth=2 /}}
++{{/box}}
--[[Kompetenzen.K4]] Ich kann Graphen von Potenzfunktionen skizzieren
--[[Kompetenzen.K1]] [[Kompetenzen.K5]] Ich kann die Eigenschaften von Potenzfunktionen ausgehend von den Funktionstermen erläutern
--[[Kompetenzen.K1]] [[Kompetenzen.K4]] Ich kann die Eigenschaften von Potenzfunktionen ausgehend von den Funktionsgraphen erläutern
--[[Kompetenzen.K1]] Ich kann den Stetigkeitsbegriff anschaulich anhand der Graphen von Potenzfunktionen erläutern
--
--Verhalten +/- oo
--Verhalten nahe Definitionslücke
--Asymptoten
--Symmetrie
--Stetigkeit
--
--{{aufgabe id="Skizzieren" afb="I" kompetenzen="" quelle="Holger Engels" cc="BY-SA"}}
--Skizziere die Graphen der Funktionen //f// und //g// mit {{formula}}f(x)=x^3{{/formula}} und {{formula}}g(x) = x^{1/3}{{/formula}} in ein gemeinsames Koordinatensystem, dessen x- und y-Achse jeweils von {{formula}}[-8; +8]{{/formula}} geht.
--{{/aufgabe}}
--
--{{aufgabe id="D und W" afb="I" kompetenzen="" quelle="Holger Engels" cc="BY-SA"}}
--Gib jeweils den Definitions- und den Wertebereich an:
--1. {{formula}}f(x)=\frac{1}{x-2}+1{{/formula}}
--1. {{formula}}g(x)=\sqrt{x+2}-1{{/formula}}
--{{/aufgabe}}
--
--{{aufgabe id="Eigenschaften" afb="I" kompetenzen="K1, K5" quelle="??" cc="BY-SA"}}
--Bestimme zu den unten genannten Funktionen den (1) Globalverlauf, die (2) Symmetrie, den (3) Definitions- und den (4) Wertebereich und gegebenenfalls (5) waagerechte und senkrechte Asymptoten.
--
--(% style="list-style: alphastyle" %)
--1. Das Schaubild der Funktion g ist eine Parabel vierter Ordnung mit dem Scheitel {{formula}}S(-2|  3){{/formula}}, die um den Streckungsfaktor {{formula}}\frac{1}{2}{{/formula}} in y-Richtung gestreckt wurde.
--1. Die Funktion h ist eine Potenzfunktion mit {{formula}}h(x) = \frac{-3}{x-2}+4{{/formula}}
--{{/aufgabe}}
--
--{{aufgabe id="Venn - Eigenschaften" afb="II" kompetenzen="K2, K4, K5" quelle="Holger Engels" cc="BY-SA" zeit="8"  tags="problemlösen"}}
--[[image:venn.svg|| width="500" style="float: left"]]
--Gib für jedes Feld **A** .. **H** eine passende Funktion {{formula}}f(x)=a\cdot x^n{{/formula}} an. Sollte ein Feld nicht gefüllt werden können, begründe bitte, warum es nicht geht.
--
--(% style="width: calc(100% - 500px); min-width: 300px" %)
--|= A |
--|= B |
--|= C |
--|= D |
--|= E |
--|= F |
--|= G |
--|= H |
--
--**Zusatzaufgabe:** Finde möglichst einfache/ komplexe Lösungen.
--{{/aufgabe}}
--
--{{aufgabe id="Stetigkeit" afb="II" kompetenzen="" quelle="Martin Rathgeb, Holger Engels" cc="BY-SA" zeit="5"}}
--Sascha behauptet, die Funktion //f// mit {{formula}}f(x) = \frac{1}{x}{{/formula}} sei auf ihrem maximalen Definitionsbereich nicht stetig, weil man ihren Graphen nicht ohne Absetzen zeichnen kann. Nimm dazu Stellung!
--{{/aufgabe}}
--
--
--
++Die Schülerinnen und Schüler skizzieren Graphen von Potenzfunktionen. Sie ermitteln die Eigenschaften von Potenzfunktionen ausgehend von den Funktionstermen und Funktionsgraphen und erläutern den Stetigkeitsbegriff anschaulich anhand der Graphen von Potenzfunktionen.

Stetigkeit ee.svg

Author

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1		-XWiki.holgerengels

Größe

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1		-17.7 KB

Inhalt

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Stetigkeit ei.svg

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1		-XWiki.holgerengels

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Stetigkeit ie.svg

Author

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1		-XWiki.holgerengels

Größe

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Inhalt

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Stetigkeit lee.svg

Author

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1		-XWiki.holgerengels

Größe

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venn.svg

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Änderungen von Dokument BPE 2.1 Funktionstypen und deren Eigenschaften

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