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Änderungen von Dokument BPE 12.3 Potenzfunktion

Zuletzt geändert von Simone Schuetze am 2025/12/18 14:49
Von Version 41.1
bearbeitet von Sandra Vogt
am 2025/12/18 10:08
Änderungskommentar: Neues Bild Funktion h.svg hochladen
Auf Version 18.1
bearbeitet von Simone Schuetze
am 2025/12/18 09:18
Änderungskommentar: Es gibt keinen Kommentar für diese Version

Zusammenfassung

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Dokument-Autor
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1 -XWiki.sandravogt
1 +XWiki.simoneschuetze
Inhalt
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54 54  Gegeben ist das Schaubild einer Potenzfunktion mit folgenden Eigenschaften:
55 55  
56 56  (% style="list-style: disc" %)
57 -- Das Schaubild ist achsensymmetrisch zur y-Achse.
57 +- Das Schaubild ist achsensymmetrisch zur $y$-Achse.
58 58  - Die Funktion ist für {{formula}}x=0{{/formula}} nicht definiert.
59 59  - Alle Funktionswerte sind positiv.
60 60  
61 -Entscheide begründet, ob die nachfolgenden Funktionsterme zu dem beschriebenen Schaubild passen können.
61 +\medskip
62 62  
63 +\textbf{Entscheide begründet}, ob die nachfolgenden Funktionsterme zu dem beschriebenen Schaubild passen können.
64 +
63 63  (% style="list-style: alphastyle" %)
64 64  1. {{formula}}f(x)=x^2{{/formula}}
65 65  1. {{formula}}f(x)=x^4{{/formula}}
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66 66  1. {{formula}}f(x)=x^{-1}{{/formula}}
67 67  1. {{formula}}f(x)=x^{-2}{{/formula}}
68 68  
69 -{{/aufgabe}}
71 +\medskip
70 70  
71 -{{aufgabe id="Kritisch Stellung nehmen" afb="II" kompetenzen="K1, K6" zeit="4" quelle="Team KS Offenburg"}}
72 -Ein Schüler behauptet:
73 - „Je größer der Exponent einer Potenzfunktion ist, desto steiler ist der Graph überall.“
74 -
75 -Nimm kritisch Stellung zu dieser Aussage.
76 -Tipp: Du kannst bspw. auch mithilfe eines konkreten Beispiels einer Potenzfunktion Stellung nehmen.
73 +\textbf{Begründe deine Entscheidung jeweils}, indem du die Definitionsmenge, die Wertemenge und die Symmetrie der Funktion berücksichtigst.
77 77  {{/aufgabe}}
78 78  
79 -{{aufgabe id="Prozesse Schaubildern zuordnen" afb="II" kompetenzen="K1, K3, K4, K6" zeit="8" quelle="Team KS Offenburg"}}
80 -Ordne jedem **Prozess (I bis IV)** das zugehörige **Schaubild** oder den zugehörigen **Funktionsterm** zu.
81 -Begründe jede deiner Zuordnung mathematisch. Gehe dabei auf folgende Punkte ein:
82 -* Wie wächst/fällt der Graph, wenn x größer wird?
83 -* Ist der Graph symmetrisch?
84 -* Was passiert bei kleinen x-Werten, besonders in der Nähe von x = 0?
85 -* Gibt es "verbotene" Werte oder eine Stelle, an der der Graph nicht definiert ist?
86 86  
87 -(%class="border%)
88 -|**Prozess I – Gaming-Display**\\
89 -Die **Fläche eines quadratischen Displays** hängt von der **Seitenlänge** ab.|{{formula}}f(x) = x^2{{/formula}}
90 -|**Prozess II – E-Scooter**\\
91 -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"]]
92 -|**Prozess III – WLAN-Signal**\\
93 -Mit wachsendem **Abstand zum Router** wird das **Signal schwächer**, verschwindet aber nie ganz.|
94 -|**Prozess IV – Social Media**\\
95 -Der **Rechenaufwand** zur Auswertung von **Interaktionen** wächst extrem schnell.|{{formula}}k(x) = x^{-1}{{/formula}}
96 -{{/aufgabe}}
97 97  
98 98  
99 -
100 -
101 101  {{seitenreflexion bildungsplan="" kompetenzen="" anforderungsbereiche="" kriterien="" menge=""/}}
102 102  
Funktion g.svg
Author
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1 -XWiki.sandravogt
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