Änderungen von Dokument BPE 12.3 Potenzfunktion
Zuletzt geändert von Simone Schuetze am 2025/12/18 14:49
Von Version 4.1
bearbeitet von Martina Wagner
am 2025/03/26 10:29
am 2025/03/26 10:29
Änderungskommentar:
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Auf Version 15.1
bearbeitet von Simone Schuetze
am 2025/12/18 09:01
am 2025/12/18 09:01
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Zusammenfassung
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Seiteneigenschaften (2 geändert, 0 hinzugefügt, 0 gelöscht)
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Anhänge (0 geändert, 3 hinzugefügt, 0 gelöscht)
Details
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... ... @@ -1,13 +1,55 @@ 1 1 {{seiteninhalt/}} 2 2 3 - 4 4 [[Kompetenzen.K4]] [[Kompetenzen.K5]] Ich kann die Eigenschaften von Potenzfunktionen und deren Graphen untersuchen . 5 5 [[Kompetenzen.K4]] [[Kompetenzen.K5]] Ich kann zwischen den verschiedenen Darstellungsformen wechseln. 6 6 6 +{{lehrende}} 7 +**Unterrichtsidee** [[Hyperbel aus Rechtecken mit gleichem Flächeninhalt>>Klasse 10.BPE_12L.Hyperbel aus Rechtecken gleichen Flächeninhalts.WebHome]] 8 +{{/lehrende}} 7 7 8 -{{aufgabe id="Lalala" afb="I" kompetenzen="K5" quelle="Mathebrücke" zeit="2" cc="by-sa" tags="mathebrücke"}} 9 -Aufgabentext 10 +{{aufgabe id="Erkunden - Gerader Exponent" afb="I" kompetenzen="K4,K5" zeit="12" quelle="Holger Engels, Martin Rathgeb"}} 11 +Gegeben sind drei Funktionsgleichungen {{formula}}f(x)=x^2{{/formula}} und {{formula}}h(x)=x^{-2}{{/formula}}. 12 +(% style="list-style: alphastyle" %) 13 +1. Gib jeweils den maximalen Definitionsbereich mit zugehörigem Wertebereich an. 14 +1. Skizziere jeweils den Graphen der Funktion ggf. mit Asymptoten; benutze dafür ein gemeinsames Koordinatensystem, dessen x-Achse von {{formula}}[-3; +3]{{/formula}} geht. 15 +1. Beschreibe die Symmetrien, die bei den Graphen bzw. zwischen den Graphen erkennbar sind. 10 10 {{/aufgabe}} 11 11 18 +{{aufgabe id="Erkunden - Ungerader Exponent" afb="I" kompetenzen="K4,K5" zeit="12" quelle="Holger Engels, Martin Rathgeb"}} 19 +Gegeben sind drei Funktionsgleichungen {{formula}}f(x)=x^3{{/formula}} und {{formula}}h(x)=x^{-3}{{/formula}}. 20 +(% style="list-style: alphastyle" %) 21 +1. Gib jeweils den maximalen Definitionsbereich mit zugehörigem Wertebereich an. 22 +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. 23 +1. Beschreibe die Symmetrien, die bei den Graphen bzw. zwischen den Graphen erkennbar sind. 24 +{{/aufgabe}} 25 + 26 +{{aufgabe id="Venn - Eigenschaften" afb="II" kompetenzen="K2, K4, K5" zeit="8" quelle="Holger Engels" cc="BY-SA" tags="problemlösen"}} 27 +[[image:Venn Potenzfunktionen Mittelstufe.svg|| width="500" style="float: left"]] 28 +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. 29 + 30 +(% style="width: calc(100% - 500px); min-width: 300px" %) 31 +|= A | 32 +|= B | 33 +|= C | 34 +|= D | 35 +{{/aufgabe}} 36 + 37 +{{aufgabe id="D und W aus Gleichung und Graph" afb="I" kompetenzen="K4,K5" quelle="Martin Rathgeb" cc="BY-SA" zeit="10"}} 38 +| ((( 39 +a) Gib den maximalen Definitionsbereich mit zugehörigem Wertebereich an! 40 +{{formula}}f(x) = \frac{1}{x}{{/formula}} 41 +))) | ((( 42 +b) Gib den maximalen Definitionsbereich mit zugehörigem Wertebereich an! 43 +{{formula}}f(x) = \x^{-2}{{/formula}} 44 +))) 45 +| (((c) Markiere den zum Definitionsbereich passenden Wertebereich im Graphen! 46 +[[image:D und W - Kubische.svg||style="height:250px"]] 47 +))) | ((( 48 +d) Gib den maximalen Definitionsbereich mit zugehörigem Wertebereich an! 49 +[[image:D und W - Parabel.svg||style="height:250px"]] 50 +))) 51 +{{/aufgabe}} 52 + 53 + 12 12 {{seitenreflexion bildungsplan="" kompetenzen="" anforderungsbereiche="" kriterien="" menge=""/}} 13 13
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