Änderungen von Dokument BPE 2.1 Funktionstypen und deren Eigenschaften

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

Von 24.2 nach 25.1 Von 63.1 nach 64.1

Von Version 25.1

bearbeitet von Holger Engels
am 2024/10/04 18:32

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Auf Version 63.1

bearbeitet von Martin Rathgeb
am 2024/10/14 15:53

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Zusammenfassung

Seiteneigenschaften (2 geändert, 0 hinzugefügt, 0 gelöscht)
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Seiteneigenschaften

Dokument-Autor

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--XWiki.holgerengels
++XWiki.martinrathgeb

Inhalt

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  [[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
--Skizzieren
  Verhalten +/- oo
  Verhalten nahe Definitionslücke
  Asymptoten
  Symmetrie
--Definitions- und Wertebereich
  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 //[-8; 8]// geht.
++{{aufgabe id="Erkunden - Gerader Parameter" afb="I" kompetenzen="" quelle="Holger Engels, Martin Rathgeb" cc="BY-SA"}}
++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 Definitionsbereich mit zugehörigem Wertebereich an und skizziere die Graphen der Funktionen ggf. mit ihren Asymptoten in ein gemeinsames Koordinatensystem, dessen x-Achse von {{formula}}[-3; +3]{{/formula}} geht. - Erkennst du bei einem Graphen bzw. zwischen zwei Graphen eine Symmetrie?
  {{/aufgabe}}
++{{aufgabe id="Erkunden - Ungerader Parameter" afb="I" kompetenzen="" quelle="Holger Engels, Martin Rathgeb" cc="BY-SA"}}
++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 mit zugehörigem Wertebereich an und 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. - Erkennst du bei einem Graphen bzw. zwischen zwei Graphen eine Symmetrie?
++{{/aufgabe}}
++
++{{aufgabe id="D und W" afb="I" kompetenzen="" quelle="Holger Engels, Martin Rathgeb" cc="BY-SA"}}
++Gib jeweils den maximalen Definitionsbereich mit zugehörigem Wertebereich an und skizziere die Graphen der Funktionen ggf. mit ihren Asymptoten:
++
++(% style="list-style: alphastyle" %)
++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.
++Bestimme zu den unten genannten Funktionen (1) den maximalen Definitionsbereich mit (2) zugehörigem Wertebereich, (3) den Globalverlauf, (4) die Symmetrie und gegebenenfalls (5) waagerechte und senkrechte Asymptoten.
  (% style="list-style: alphastyle" %)
 . 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}}
++1. Die Funktion h ist eine transformierte Potenzfunktion mit {{formula}}h(x) = \frac{-3}{x-2}+4{{/formula}}.
  {{/aufgabe}}
--{{aufgabe id="Venn - Eigenschaften" afb="II" kompetenzen="" quelle="Holger Engels" cc="BY-SA"}}
++{{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 Potenzfunktion //f// an. Sollte ein Feld nicht gefüllt werden können, begründe bitte, warum es nicht geht.
++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 |
@@ -42,6 +42,15 @@
  **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}}
++{{aufgabe id="Stetigkeitsbetrachtungen" afb="II" kompetenzen="" quelle="Martin Rathgeb, Holger Engels" cc="BY-SA" zeit="5"}}
++Beurteile für jedes Schaubild, ob der Graph zu einer (zusammengesetzten) Funktion gehören kann und ob diese im dargestellten stetig sind!
++[[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"]]
++[[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:
++⬤ schließt den Punkt ein
++⭘ schließt ihn aus)))
++{{/aufgabe}}
--

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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Stetigkeit ie.svg

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Stetigkeit ii.svg

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Änderungen von Dokument BPE 2.1 Funktionstypen und deren Eigenschaften

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