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Zuletzt geändert von Holger Engels am 2025/03/31 21:42
Von Version 33.1
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am 2024/10/14 12:10
Änderungskommentar: Neues Bild Stetigkeit lie.svg hochladen
Auf Version 24.2
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Seiteneigenschaften
Inhalt
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5 5  [[Kompetenzen.K1]] [[Kompetenzen.K4]] Ich kann die Eigenschaften von Potenzfunktionen ausgehend von den Funktionsgraphen erläutern
6 6  [[Kompetenzen.K1]] Ich kann den Stetigkeitsbegriff anschaulich anhand der Graphen von Potenzfunktionen erläutern
7 7  
8 -Verhalten +/- oo
9 -Verhalten nahe Definitionslücke
10 -Asymptoten
11 -Symmetrie
12 -Stetigkeit
8 +Zuordnen, Skizzieren
13 13  
14 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.
11 +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.
16 16  {{/aufgabe}}
17 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 24  {{aufgabe id="Eigenschaften" afb="I" kompetenzen="K1, K5" quelle="??" cc="BY-SA"}}
25 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 26  
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29 29  1. Die Funktion h ist eine Potenzfunktion mit {{formula}}h(x) = \frac{-3}{x-2}+4{{/formula}}
30 30  {{/aufgabe}}
31 31  
32 -{{aufgabe id="Venn - Eigenschaften" afb="II" kompetenzen="K2, K4, K5" quelle="Holger Engels" cc="BY-SA" zeit="8" tags="problemlösen"}}
22 +{{aufgabe id="Venn - Eigenschaften" afb="II" kompetenzen="" quelle="Holger Engels" cc="BY-SA"}}
33 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.
24 +Gib für jedes Feld **A** .. **H** eine passende Potenzfunktion //f// an. Sollte ein Feld nicht gefüllt werden können, begründe bitte, warum es nicht geht.
35 35  
36 36  (% style="width: calc(100% - 500px); min-width: 300px" %)
37 37  |= A |
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46 46  **Zusatzaufgabe:** Finde möglichst einfache/ komplexe Lösungen.
47 47  {{/aufgabe}}
48 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 52  
53 53  
54 54  
Stetigkeit lie.svg
Author
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1 -XWiki.holgerengels
Größe
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1 -45.0 KB
Inhalt
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