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Auf Version 2.1
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Details

Seiteneigenschaften
Titel
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1 -BPE 2.1 Funktionstypen und deren Eigenschaften
1 +Funktionstypen und deren Eigenschaften
Übergeordnete Seite
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1 -Eingangsklasse.WebHome
1 +Main.WebHome
Dokument-Autor
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1 -XWiki.holgerengels
1 +XWiki.holger
Inhalt
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1 -{{seiteninhalt/}}
1 +{{box cssClass="floatinginfobox" title="**Contents**"}}
2 +{{toc start=2 depth=2 /}}
3 +{{/box}}
2 2  
3 -[[Kompetenzen.K4]] Ich kann Graphen von Potenzfunktionen skizzieren
4 -[[Kompetenzen.K1]] [[Kompetenzen.K5]] Ich kann die Eigenschaften von Potenzfunktionen ausgehend von den Funktionstermen erläutern
5 -[[Kompetenzen.K1]] [[Kompetenzen.K4]] Ich kann die Eigenschaften von Potenzfunktionen ausgehend von den Funktionsgraphen erläutern
6 -[[Kompetenzen.K1]] Ich kann den Stetigkeitsbegriff anschaulich anhand der Graphen von Potenzfunktionen erläutern
7 -
8 -Verhalten +/- oo
9 -Verhalten nahe Definitionslücke
10 -Asymptoten
11 -Symmetrie
12 -Stetigkeit
13 -
14 -{{aufgabe id="Skizzieren" afb="I" kompetenzen="" quelle="Holger Engels" cc="BY-SA"}}
15 -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.
16 -{{/aufgabe}}
17 -
18 -{{aufgabe id="D und W" afb="I" kompetenzen="" quelle="Holger Engels" cc="BY-SA"}}
19 -Gib jeweils den Definitions- und den Wertebereich an:
20 -1. {{formula}}f(x)=\frac{1}{x-2}+1{{/formula}}
21 -1. {{formula}}g(x)=\sqrt{x+2}-1{{/formula}}
22 -{{/aufgabe}}
23 -
24 -{{aufgabe id="Eigenschaften" afb="I" kompetenzen="K1, K5" quelle="??" cc="BY-SA"}}
25 -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.
26 -
27 -(% style="list-style: alphastyle" %)
28 -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.
29 -1. Die Funktion h ist eine Potenzfunktion mit {{formula}}h(x) = \frac{-3}{x-2}+4{{/formula}}
30 -{{/aufgabe}}
31 -
32 -{{aufgabe id="Venn - Eigenschaften" afb="II" kompetenzen="K2, K4, K5" quelle="Holger Engels" cc="BY-SA" zeit="8" tags="problemlösen"}}
33 -[[image:venn.svg|| width="500" style="float: left"]]
34 -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.
35 -
36 -(% style="width: calc(100% - 500px); min-width: 300px" %)
37 -|= A |
38 -|= B |
39 -|= C |
40 -|= D |
41 -|= E |
42 -|= F |
43 -|= G |
44 -|= H |
45 -
46 -**Zusatzaufgabe:** Finde möglichst einfache/ komplexe Lösungen.
47 -{{/aufgabe}}
48 -
49 -{{aufgabe id="Stetigkeit" afb="II" kompetenzen="" quelle="Martin Rathgeb, Holger Engels" cc="BY-SA" zeit="5"}}
50 -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!
51 -{{/aufgabe}}
52 -
53 -
54 -
5 +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
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1 -17.7 KB
Inhalt
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Stetigkeit ei.svg
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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 ii.svg
Author
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1 -XWiki.holgerengels
Größe
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1 -20.1 KB
Inhalt
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