Änderungen von Dokument BPE 12.3 Potenzfunktion

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

Von 9.1 nach 8.1 Von 44.1 nach 43.1

Von Version 43.1

bearbeitet von Sandra Vogt
am 2025/12/18 10:09

Änderungskommentar: Es gibt keinen Kommentar für diese Version

Auf Version 9.1

bearbeitet von Holger Engels
am 2025/12/12 07:03

Änderungskommentar: Neues Bild Venn Potenzfunktionen Mittelstufe.svg hochladen

Rohform
Im Layout

Zusammenfassung

Seiteneigenschaften (2 geändert, 0 hinzugefügt, 0 gelöscht)
Anhänge (0 geändert, 0 hinzugefügt, 4 gelöscht)

Details

Seiteneigenschaften

Dokument-Autor

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--XWiki.sandravogt
++XWiki.holgerengels

Inhalt

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  **Unterrichtsidee** [[Hyperbel aus Rechtecken mit gleichem Flächeninhalt>>Klasse 10.BPE_12L.Hyperbel aus Rechtecken gleichen Flächeninhalts.WebHome]]
  {{/lehrende}}
--{{aufgabe id="Definitions- und Wertemenge 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) = x^{-2}{{/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}}
--
  {{aufgabe id="Erkunden - Gerader Exponent" afb="I" kompetenzen="K4,K5" zeit="12" quelle="Holger Engels, Martin Rathgeb"}}
--Gegeben sind zwei Funktionsgleichungen {{formula}}f(x)=x^2{{/formula}} und {{formula}}h(x)=x^{-2}{{/formula}}.
++Gegeben sind drei Funktionsgleichungen {{formula}}f(x)=x^2{{/formula}} und {{formula}}h(x)=x^{-2}{{/formula}}.
  (% style="list-style: alphastyle" %)
 . Gib jeweils den maximalen Definitionsbereich mit zugehörigem Wertebereich an.
 . Skizziere jeweils den Graphen der Funktion ggf. mit Asymptoten; benutze dafür ein gemeinsames Koordinatensystem, dessen x-Achse von {{formula}}[-3; +3]{{/formula}} geht.
@@ -39,71 +39,5 @@
 . 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="Entscheiden – Potenzfunktionen" afb="II" kompetenzen="K2,K4,K5" zeit="8" quelle="Team KS Offenburg"}}
--Gegeben ist das Schaubild einer Potenzfunktion mit folgenden Eigenschaften:
--
--(% style="list-style: disc" %)
--- Das Schaubild ist achsensymmetrisch zur y-Achse.
--- Die Funktion ist für {{formula}}x=0{{/formula}} nicht definiert.
--- Alle Funktionswerte sind positiv.
--
--Entscheide begründet, ob die nachfolgenden Funktionsterme zu dem beschriebenen Schaubild passen können.
--
--(% style="list-style: alphastyle" %)
--1. {{formula}}f(x)=x^2{{/formula}}
--1. {{formula}}f(x)=x^4{{/formula}}
--1. {{formula}}f(x)=x^{-1}{{/formula}}
--1. {{formula}}f(x)=x^{-2}{{/formula}}
--
--{{/aufgabe}}
--
--{{aufgabe id="Kritisch Stellung nehmen" afb="II" kompetenzen="K1, K6" zeit="4" quelle="Team KS Offenburg"}}
--Ein Schüler behauptet:
--  „Je größer der Exponent einer Potenzfunktion ist, desto steiler ist der Graph überall.“
--
--Nimm kritisch Stellung zu dieser Aussage.
--Tipp: Du kannst bspw. auch mithilfe eines konkreten Beispiels einer Potenzfunktion Stellung nehmen.
--{{/aufgabe}}
--
--{{aufgabe id="Prozesse Schaubildern zuordnen" afb="II" kompetenzen="K1, K3, K4, K6" zeit="8" quelle="Team KS Offenburg"}}
--Ordne jedem **Prozess (I bis IV)** das zugehörige **Schaubild** oder den zugehörigen **Funktionsterm** zu.
--Begründe jede deiner Zuordnung mathematisch. Gehe dabei auf folgende Punkte ein:
--* Wie wächst/fällt der Graph, wenn x größer wird?
--* Ist der Graph symmetrisch?
--* Was passiert bei kleinen x-Werten, besonders in der Nähe von x = 0?
--* Gibt es "verbotene" Werte oder eine Stelle, an der der Graph nicht definiert ist?
--
--(%class="border%)
--|**Prozess I – Gaming-Display**\\
--Die **Fläche eines quadratischen Displays** hängt von der **Seitenlänge** ab.|{{formula}}f(x) = x^2{{/formula}}
--|**Prozess II – E-Scooter**\\
--Die **Belastung des Motors** steigt mit der **Leistungseinstellung**: bei kleinen Werten wenig, bei großen Werten sehr stark.|[[image:Funktion g.svg|| width="500" style="float: left"]]
--|**Prozess III – WLAN-Signal**\\
--Mit wachsendem **Abstand zum Router** wird das **Signal schwächer**, verschwindet aber nie ganz.|[[image:Funktion h.svg|| width="500" style="float: left"]]
--|**Prozess IV – Social Media**\\
--Der **Rechenaufwand** zur Auswertung von **Interaktionen** wächst extrem schnell.|{{formula}}k(x) = x^{-1}{{/formula}}
--{{/aufgabe}}
--
--{{aufgabe id="Untersuchen – Annäherung an Achsen" afb="III" kompetenzen="K4,K5,K6" zeit="10" quelle="Team KS Offenburg"}}
--Zwei Potenzfunktionen {{formula}}f(x)=x^k{{/formula}} und {{formula}}g(x)=x^m{{/formula}} mit negativen ganzzahligen Exponenten haben Schaubilder, die sich der x-Achse annähern.
--
--(% style="list-style: alphastyle" %)
--1. Entwickle ein Kriterium, mit dem man entscheiden kann, welcher der beiden Graphen für große {{formula}}|x|{{/formula}} schneller gegen die x-Achse fällt. Erkläre deine Überlegung.
--1. Überprüfe, ob dieses Kriterium auch dafür geeignet ist zu entscheiden, welcher der beiden Graphen sich für {{formula}}x\to 0{{/formula}} schneller der y-Achse annähert. Begründe deine Entscheidung.
--{{/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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D und W - Parabel.svg

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1		-XWiki.simoneschuetze

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Funktion g.svg

Author

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1		-XWiki.sandravogt

Größe

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1		-22.3 KB

Inhalt

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