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Zuletzt geändert von Holger Engels am 2025/08/07 05:24
Von Version 45.1
bearbeitet von Holger Engels
am 2024/10/14 10:22
Änderungskommentar: Neues Bild Stetigkeit lee.svg hochladen
Auf Version 61.1
bearbeitet von Martin Rathgeb
am 2024/10/14 13:51
Änderungskommentar: Es gibt keinen Kommentar für diese Version

Zusammenfassung

Details

Seiteneigenschaften
Dokument-Autor
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1 -XWiki.holgerengels
1 +XWiki.martinrathgeb
Inhalt
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11 11  Symmetrie
12 12  Stetigkeit
13 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.
14 +{{aufgabe id="Erkunden - Gerader Parameter" afb="I" kompetenzen="" quelle="Holger Engels, Martin Rathgeb" cc="BY-SA"}}
15 +Gib zu den Funktionsgleichungen {{formula}}f(x)=x^2{{/formula}}, {{formula}}g(x)=x^{1/2}{{/formula}} und {{formula}}h(x)=x^{-2}{{/formula}} jeweils den maximalen Definitions- und den maximalen Wertebereich an; skizziere die Graphen der Funktionen ggf. mit ihren Asymptoten in ein gemeinsames Koordinatensystem, dessen x-Achse von {{formula}}[-3; +3]{{/formula}} geht.
16 +Erkennst du bei einem Graphen bzw. zwischen zwei Graphen eine Symmetrie?
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:
19 +{{aufgabe id="Erkunden - Ungerader Parameter" afb="I" kompetenzen="" quelle="Holger Engels, Martin Rathgeb" cc="BY-SA"}}
20 +Gib zu den Funktionsgleichungen {{formula}}f(x)=x^3{{/formula}}, {{formula}}g(x)=x^{1/3}{{/formula}} und {{formula}}h(x)=x^{-3}{{/formula}} jeweils den maximalen Definitionsbereich, den zugehörigen Wertebereich an; skizziere die Graphen der Funktionen ggf. mit ihren Asymptoten in ein gemeinsames Koordinatensystem, dessen x- und y-Achse jeweils von {{formula}}[-8; +8]{{/formula}} geht.
21 +Erkennst du bei einem Graphen bzw. zwischen zwei Graphen eine Symmetrie?
22 +{{/aufgabe}}
23 +
24 +{{aufgabe id="D und W" afb="I" kompetenzen="" quelle="Holger Engels, Martin Rathgeb" cc="BY-SA"}}
25 +Gib jeweils den maximalen Definitionsbereich, den zugehörigen Wertebereich an; skizziere die Graphen der Funktionen ggf. mit ihren Asymptoten:
26 +
27 +(% style="list-style: alphastyle" %)
20 20  1. {{formula}}f(x)=\frac{1}{x-2}+1{{/formula}}
21 21  1. {{formula}}g(x)=\sqrt{x+2}-1{{/formula}}
22 22  {{/aufgabe}}
23 23  
24 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.
33 +Bestimme zu den unten genannten Funktionen (1) den maximalen Definitionsbereich, (2) den zugehörigen Wertebereich, (3) den Globalverlauf, (4) die Symmetrie und gegebenenfalls (5) waagerechte und senkrechte Asymptoten.
26 26  
27 27  (% style="list-style: alphastyle" %)
28 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}}
37 +1. Die Funktion h ist eine transformierte Potenzfunktion mit {{formula}}h(x) = \frac{-3}{x-2}+4{{/formula}}.
30 30  {{/aufgabe}}
31 31  
32 32  {{aufgabe id="Venn - Eigenschaften" afb="II" kompetenzen="K2, K4, K5" quelle="Holger Engels" cc="BY-SA" zeit="8" tags="problemlösen"}}
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50 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 51  {{/aufgabe}}
52 52  
61 +{{aufgabe id="Stetigkeitsbetrachtungen" afb="II" kompetenzen="" quelle="Martin Rathgeb, Holger Engels" cc="BY-SA" zeit="5"}}
62 +Beurteile für jedes Schaubild, ob der Graph zu einer (zusammengesetzten) Funktion gehören kann und ob diese im dargestellten stetig sind!
63 +[[image:Stetigkeit ee.svg||style="margin: 8px"]] [[image:Stetigkeit ie.svg||style="margin: 8px"]] [[image:Stetigkeit ei.svg||style="margin: 8px"]] [[image:Stetigkeit ii.svg||style="margin: 8px"]]
64 +[[image:Stetigkeit lee.svg||style="margin: 8px"]] [[image:Stetigkeit lie.svg||style="margin: 8px"]] [[image:Stetigkeit lei.svg||style="margin: 8px"]] [[image:Stetigkeit lii.svg||style="margin: 8px"]] [[image:Stetigkeit o.svg||style="margin: 8px"]] (% style="display: inline-block" %)(((Hinweis:
65 +⬤ schließt den Punkt ein
66 +⭘ schließt ihn aus)))
67 +{{/aufgabe}}
53 53  
54 -
Stetigkeit lie.svg
Größe
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1 -45.0 KB
1 +18.3 KB
Inhalt
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