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Zuletzt geändert von Holger Engels am 2025/03/31 21:42
Von Version 25.1
bearbeitet von Holger Engels
am 2024/10/04 18:32
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Auf Version 1.1
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Zusammenfassung

Details

Seiteneigenschaften
Titel
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1 -BPE 2.1 Funktionstypen und deren Eigenschaften
1 +BPE_2_1
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 -Skizzieren
9 -Verhalten +/- oo
10 -Verhalten nahe Definitionslücke
11 -Asymptoten
12 -Symmetrie
13 -Definitions- und Wertebereich
14 -Stetigkeit
15 -
16 -{{aufgabe id="Skizzieren" afb="I" kompetenzen="" quelle="Holger Engels" cc="BY-SA"}}
17 -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 //[-8; 8]// geht.
18 -{{/aufgabe}}
19 -
20 -{{aufgabe id="Eigenschaften" afb="I" kompetenzen="K1, K5" quelle="??" cc="BY-SA"}}
21 -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.
22 -
23 -(% style="list-style: alphastyle" %)
24 -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.
25 -1. Die Funktion h ist eine Potenzfunktion mit {{formula}}h(x) = \frac{-3}{x-2}+4{{/formula}}
26 -{{/aufgabe}}
27 -
28 -{{aufgabe id="Venn - Eigenschaften" afb="II" kompetenzen="" quelle="Holger Engels" cc="BY-SA"}}
29 -[[image:venn.svg|| width="500" style="float: left"]]
30 -Gib für jedes Feld **A** .. **H** eine passende Potenzfunktion //f// an. Sollte ein Feld nicht gefüllt werden können, begründe bitte, warum es nicht geht.
31 -
32 -(% style="width: calc(100% - 500px); min-width: 300px" %)
33 -|= A |
34 -|= B |
35 -|= C |
36 -|= D |
37 -|= E |
38 -|= F |
39 -|= G |
40 -|= H |
41 -
42 -**Zusatzaufgabe:** Finde möglichst einfache/ komplexe Lösungen.
43 -{{/aufgabe}}
44 -
45 -
46 -
47 -
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.
venn.svg
Author
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1 -XWiki.holgerengels
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