Änderungen von Dokument BPE 12.3 Potenzfunktion

Zuletzt geändert von Simone Schuetze am 2025/12/18 14:49

Von 5.1 nach 4.1 Von 13.1 nach 12.1

Von Version 12.1

bearbeitet von Simone Schuetze
am 2025/12/18 08:58

Änderungskommentar: Neues Bild D und W - Kubische.svg hochladen

Auf Version 5.1

bearbeitet von Holger Engels
am 2025/06/18 06:07

Änderungskommentar: Es gibt keinen Kommentar für diese Version

Rohform
Im Layout

Zusammenfassung

Seiteneigenschaften (2 geändert, 0 hinzugefügt, 0 gelöscht)
Anhänge (0 geändert, 0 hinzugefügt, 2 gelöscht)
- D und W - Kubische.svg
- Venn Potenzfunktionen Mittelstufe.svg

Details

Seiteneigenschaften

Dokument-Autor

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--XWiki.simoneschuetze
++XWiki.holgerengels

Inhalt

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  [[Kompetenzen.K4]] [[Kompetenzen.K5]] Ich kann die Eigenschaften von Potenzfunktionen und deren Graphen untersuchen .
  [[Kompetenzen.K4]] [[Kompetenzen.K5]] Ich kann zwischen den verschiedenen Darstellungsformen wechseln.
--{{lehrende}}
--**Unterrichtsidee** [[Hyperbel aus Rechtecken mit gleichem Flächeninhalt>>Klasse 10.BPE_12L.Hyperbel aus Rechtecken gleichen Flächeninhalts.WebHome]]
--{{/lehrende}}
--
--{{aufgabe id="Erkunden - Gerader Exponent" afb="I" kompetenzen="K4,K5" zeit="12" quelle="Holger Engels, Martin Rathgeb"}}
--Gegeben sind drei Funktionsgleichungen {{formula}}f(x)=x^2{{/formula}} und {{formula}}h(x)=x^{-2}{{/formula}}.
--(% style="list-style: alphastyle" %)
--1. Gib jeweils den maximalen Definitionsbereich mit zugehörigem Wertebereich an.
--1. Skizziere jeweils den Graphen der Funktion ggf. mit Asymptoten; benutze dafür ein gemeinsames Koordinatensystem, dessen x-Achse von {{formula}}[-3; +3]{{/formula}} geht.
--1. Beschreibe die Symmetrien, die bei den Graphen bzw. zwischen den Graphen erkennbar sind.
--{{/aufgabe}}
--
--{{aufgabe id="Erkunden - Ungerader Exponent" afb="I" kompetenzen="K4,K5" zeit="12" quelle="Holger Engels, Martin Rathgeb"}}
--Gegeben sind drei Funktionsgleichungen {{formula}}f(x)=x^3{{/formula}} und {{formula}}h(x)=x^{-3}{{/formula}}.
--(% style="list-style: alphastyle" %)
--1. Gib jeweils den maximalen Definitionsbereich mit zugehörigem Wertebereich an.
--1. Skizziere jeweils die Graphen der Funktionen ggf. mit ihren Asymptoten; benutze dafür ein gemeinsames Koordinatensystem, dessen x- und y-Achse jeweils von {{formula}}[-8; +8]{{/formula}} geht.
--1. Beschreibe die Symmetrien, die bei den Graphen bzw. zwischen den Graphen erkennbar sind.
--{{/aufgabe}}
--
--{{aufgabe id="Venn - Eigenschaften" afb="II" kompetenzen="K2, K4, K5" zeit="8" quelle="Holger Engels" cc="BY-SA" tags="problemlösen"}}
--[[image:Venn Potenzfunktionen Mittelstufe.svg|| width="500" style="float: left"]]
--Gib für jedes Feld **A** .. **D** eine passende Funktion {{formula}}f(x)=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 |
--|= B |
--|= C |
--|= D |
--{{/aufgabe}}
--
--{{aufgabe id="D und W aus Gleichung und Graph" afb="I" kompetenzen="K4,K5" quelle="Martin Rathgeb" cc="BY-SA" zeit="10"}}
--| (((
--a) Gib den maximalen Definitionsbereich mit zugehörigem Wertebereich an!
--{{formula}}f(x) = \frac{1}{x}{{/formula}}
--))) | (((
--b) Gib den maximalen Definitionsbereich mit zugehörigem Wertebereich an!
--{{formula}}f(x) = \sqrt{x}{{/formula}}
--)))
--| (((c) Markiere den zum Definitionsbereich passenden Wertebereich im Graphen!
--[[image:D und W - Kubische.svg||style="height:250px"]]
--))) | (((
--d) Gib den maximalen Definitionsbereich mit zugehörigem Wertebereich an!
--[[image:D und W - Parabel.svg||style="height:250px"]]
--)))
--{{/aufgabe}}
--
--
  {{seitenreflexion bildungsplan="" kompetenzen="" anforderungsbereiche="" kriterien="" menge=""/}}

D und W - Kubische.svg

Author

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1		-XWiki.simoneschuetze

Größe

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1		-23.0 KB

Inhalt

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