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Zuletzt geändert von Holger Engels am 2025/01/10 13:45
Von Version 58.1
bearbeitet von Holger Engels
am 2024/07/19 11:41
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Auf Version 73.1
bearbeitet von Holger Engels
am 2024/07/22 14:44
Änderungskommentar: Neues Bild D und W - Kubische.svg hochladen

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8 8  
9 9  == Definition ==
10 10  
11 -{{aufgabe id="Venn" afb="I" kompetenzen="K5" quelle="[[KMap>>https://kmap.eu/app/browser/Mathematik/Funktionen/Allgemeines]]" cc="BY-SA"}}
11 +{{aufgabe id="Venn" afb="I" kompetenzen="K1,K4,K6" quelle="[[KMap>>https://kmap.eu/app/browser/Mathematik/Funktionen/Allgemeines]]" cc="BY-SA"}}
12 12  Welche der beiden Zuordnungen ist eindeutig? Überlege jeweils, ob es sich um eine Relation oder um eine Funktion handelt!
13 13  Begründe deine Entscheidung!
14 14  
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15 15  [[image:Venn Funktion.png||width="400px"]] [[image:Venn Relation.png||width="400px"]]
16 16  {{/aufgabe}}
17 17  
18 -{{aufgabe id="Baby" afb="II" kompetenzen="K1,K3,K4" quelle="Torben Würth" cc="BY-SA" zeit="15"}}
19 -In dieser Aufgabe soll die Entwicklung der Körpergröße eines weiblich Babys in Abhängigkeit vom Alter dargestellt werden.
18 +{{aufgabe id="Baby" afb="II" kompetenzen="K1,K2,K3,K4,K5,K6" quelle="Torben Würth" cc="BY-SA" zeit="15"}}
19 +In dieser Aufgabe soll die Entwicklung der Körpergröße eines weiblichen Babys in Abhängigkeit vom Alter dargestellt werden.
20 20  [[image:Achsenkreuz.svg||width="600px"]]
21 21  1. Skizziere ins Achsenkreuz eine mögliche Entwicklung.
22 22  1. Nenne die von dir gewählte Wertebereich. Begründe deine Wahl.
23 -1. Nenne die von dir gewählte Definitionsbereich Begründe deine Wahl.
23 +1. Nenne die von dir gewählte Definitionsbereich. Begründe deine Wahl.
24 24  1. Erläutere, ob dein Graph ein Funktionsgraph ist.
25 +1. Erläutere, ob die Umkehrung "Alter in Abhängigkeit von der Körpergröße" eine Funktion ist.
25 25  1. Verändern sich Definitionsbereich und Wertebereich, wenn du die Aufgabe für ein männliches Baby löst? Begründe deine Antwort.
26 26  
27 27  {{lehrende}}
28 28  **Variation für den Unterricht:**
29 -Das Potential liegt in der Besprechung der Ergebnisse [[Kompetenzen.K6]]
30 +Das Potential der Aufgabe liegt in der Besprechung der Ergebnisse [[Kompetenzen.K6]]
30 30  {{/lehrende}}
31 31  
32 32  {{/aufgabe}}
33 33  
34 -{{aufgabe id="Definitionslücke - mein Weg zur Schule ist nicht schwer" afb="II" kompetenzen="K1,K3,K4" quelle="Ute Jutt, Ronja Franke" cc="BY-SA" zeit="15"}}
35 -Stell dir vor, du möchtest die Zeit berechnen, die du benötigst, um zur Schule zu laufen.
35 +{{aufgabe id="D und W aus Gleichung und Graph" afb="I" kompetenzen="K4,K5" quelle="Martin Rathgeb" cc="BY-SA" zeit="15"}}
36 +| (((
37 +Gib den maximalen Definitions- und Wertebereich an!
38 +{{formula}}f(x) = \frac{1}{x}{{/formula}}
39 +)))|(((
40 +Gib den maximalen Definitions- und Wertebereich an!
41 +{{formula}}f(x) = \sqrt{x}{{/formula}}
42 +)))
43 +Markiere den zum Definitionsbereich passenden Wertebereich im Graphen
44 +[[image:D und W - Kubische.svg||height=300]]
45 +)))|(((
46 +Gib den maximalen Definitions- und Wertebereich an!
47 +[[image:D und W - Parabel.svg||height=300]]
48 +)))
49 +{{/aufgabe}}
50 +
51 +{{aufgabe id="D und W aus Anwendungssituation" afb="II" kompetenzen="K3,K4,K5,K6" quelle="Martin Rathgeb" cc="BY-SA" zeit="15"}}
52 +Skizziere jeweils zunächst ein Schaubild:
53 +1. Kaffee kühlt ab
54 +1. Geschwindigkeit - Bremsweg
55 +Gib jeweils einen im Sachzusammenhang passenden Definitions- und Wertebereich an. Diskutiere deine Ergebnisse mit Mitschüler*innen.
56 +{{/aufgabe}}
57 +
58 +{{aufgabe id="D und W aus unbekannter Gleichung" afb="II" kompetenzen="K4,K5" quelle="Martin Rathgeb" cc="BY-SA" zeit="15"}}
59 +Ermittle für folgende Funktionsgleichungen jeweils den maximalen Definitionsbereich mit zugehörigem Wertebereich.
60 +1. {{formula}}f(x) = \frac{1}{x-2}{{/formula}}
61 +1. {{formula}}f(x) = \sqrt{x+1}{{/formula}}
62 +1. {{formula}}f(x) = \frac{x}{x}{{/formula}}
63 +{{/aufgabe}}
64 +
65 +{{aufgabe id="Weg zur Schule" afb="II" kompetenzen="K1,K3,K4" quelle="Ute Jutt, Ronja Franke" cc="BY-SA" zeit="15"}}
66 +Stell dir vor, du möchtest die Zeit berechnen, die du benötigst, um zur Schule zu laufen.
36 36  Die Funktion {{formula}}T(x){{/formula}} gibt die benötigte Zeit in Minuten an, abhängig von der Geschwindigkeit {{formula}}x{{/formula}} in km/min.
37 37  Die Funktion könnte wie folgt definiert sein: {{formula}}T(x)= \frac{d}{x}{{/formula}}, wobei {{formula}}d{{/formula}} die Entfernung zur Schule in Kilometern ist.
38 38  Nehmen wir an, du wohnst 5 km zur Schule entfernt.
39 39  
40 -1. Erstelle die Funktion {{formula}}T(x){{/formula}}, die die benötigte Zeit in Minuten in Abhängigkeit von der Geschwindigkeit {{formula}}x{{/formula}} in km/h beschreibt.
41 -1. Bestimme die Definitionslücke der Funktion {{formula}}T(x){{/formula}}.
42 -1. Erläutere, warum es in diesem Kontext sinnvoll ist, eine Definitionslücke zu haben.
43 -1. Zeichne den Graphen der Funktion {{formula}}T(x){{/formula}} und markiere die Definitionslücke.
71 +1. Erstelle die Funktion {{formula}}T(x){{/formula}}, die die benötigte Zeit in Minuten in Abhängigkeit von der Geschwindigkeit {{formula}}x{{/formula}} in km/h beschreibt.
72 +1. Bestimme die Definitionslücke der Funktion {{formula}}T(x){{/formula}}.
73 +1. Erläutere, warum es in diesem Kontext sinnvoll ist, eine Definitionslücke zu haben.
74 +1. Zeichne den Graphen der Funktion {{formula}}T(x){{/formula}} und markiere die Definitionslücke.
75 +{{/aufgabe}}
44 44  
77 +{{aufgabe id="Erkunden unbekannte Funktionsgleichung" afb="III" kompetenzen="K1,K2,K4,K5" quelle="Martin Rathgeb" cc="BY-SA" zeit="15"}}
78 +Eine für dich unbekannte Funktionsgleichung lautet {{formula}}f(x) = \sin^{-1}(x){{/formula}}.
79 +Beschreibe eine Möglichkeit, den maximalen Definitionsbereich (als Teilmenge von {{formula}}[-2;+2]{{/formula}}) mit zugehörigem Wertebereich zu ermitteln. Bestimme die beiden Bereiche.
45 45  {{/aufgabe}}
81 +
82 +{{lehrende}}
83 +AFB III kann an dieser Stelle noch nicht sinnvoll erreicht werden, weil nur einfache Funktionstypen und keine komplexen Verknüpfungen bekannt sind
84 +{{/lehrende}}
85 +
86 +{{seitenreflexion bildungsplan="5" kompetenzen="5" anforderungsbereiche="5" kriterien="4" menge="4"/}}
D und W - Kubische.svg
Author
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1 +XWiki.holgerengels
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