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Zuletzt geändert von Martin Rathgeb am 2025/04/06 23:13
Von Version 81.1
bearbeitet von Holger Engels
am 2024/12/17 20:07
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Auf Version 70.1
bearbeitet von Holger Engels
am 2024/11/22 09:02
Änderungskommentar: Neues Bild Bedingungen g.svg hochladen

Zusammenfassung

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Inhalt
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1 -{{seiteninhalt/}}
1 +{{box cssClass="floatinginfobox" title="**Contents**"}}
2 +{{toc start=2 depth=2 /}}
3 +{{/box}}
2 2  
5 +=== Kompetenzen ===
6 +
3 3  [[Kompetenzen.K5]] Ich kann den passenden Ansatz für die Ermittlung eines Funktionsterms anhand gegebener Bedingungen bestimmen
4 4  [[Kompetenzen.K4]] [[Kompetenzen.K5]] Ich kann den Funktionsterm anhand verbal gegebener Bedingungen aufstellen
5 5  [[Kompetenzen.K4]] [[Kompetenzen.K5]] Ich kann den Funktionsterm anhand tabellarisch gegebener Bedingungen aufstellen
6 6  [[Kompetenzen.K4]] [[Kompetenzen.K5]] Ich kann den Funktionsterm anhand eines Schaubilds aufstellen
7 7  
8 -{{aufgabe id="Änderungen sind bemerkenswert" afb="I" kompetenzen="K2, K4, K5" quelle="Martin Rathgeb, Martin Stern" zeit="" cc="by-sa"}}
12 +{{aufgabe id="Änderungen sind bemerkenswert" afb="I" kompetenzen="K2, K4, K5" quelle="Martin Rathgeb, Martin Stern" zeit="" cc="" }}
9 9  (% class="border slim" %)
10 10  Liegen die Punkte auf einer Parabel?
11 11  (% class="border slim" %)
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14 14  |{{formula}}f_2(x){{/formula}}|1|3|5
15 15  {{/aufgabe}}
16 16  
17 -{{aufgabe id="Parabel aus zwei Punktproben mit Zusatzinformation" afb="II" kompetenzen="K2, K4, K5" quelle="Martin Rathgeb, Martin Stern" zeit="" cc="by-sa"}}
21 +{{aufgabe id="Parabel aus zwei Punktproben mit Zusatzinformation" afb="II" kompetenzen="K2, K4, K5" quelle="Martin Rathgeb, Martin Stern" zeit="" cc="" }}
18 18  //Scheitel(punkts)form.// Bestimme aus folgenden Wertetabellen (je zwei Wertepaare) mit Zusatzinformation jeweils die quadratische Funktion.
19 19  (% class="border slim" %)
20 20  |{{formula}}x{{/formula}}|1|3|
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24 24  |{{formula}}f_4(x){{/formula}}|2|1|{{formula}}y_s=2{{/formula}}
25 25  {{/aufgabe}}
26 26  
27 -{{aufgabe id="Parabel aus drei Punktproben" afb="II" kompetenzen="K2, K4, K5" quelle="Martin Rathgeb, Martin Stern" zeit="" cc="by-sa"}}
31 +{{aufgabe id="Parabel aus drei Punktproben" afb="II" kompetenzen="K2, K4, K5" quelle="Martin Rathgeb, Martin Stern" zeit="" cc="" }}
28 28  //Haupt-, Scheitel(punkts)-, Produktform.// Bestimme aus folgenden Wertetabellen (je drei Wertepaare) jeweils die quadratische Funktion.
29 29  (% class="border slim" %)
30 30  |{{formula}}x{{/formula}}|1|2|3
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34 34  |{{formula}}f_4(x){{/formula}}|-2|0|-2
35 35  {{/aufgabe}}
36 36  
37 -{{aufgabe id="Produktdarstellung" afb="I" kompetenzen="K1, K4, K5" quelle="Miriam Erdmann" zeit="5" cc="" }}
41 +{{aufgabe id="Produktdarstellung" afb="I" kompetenzen="K4, K5" quelle="Miriam Erdmann" zeit="5" cc="" }}
38 38  Gegeben ist das Schaubild der Funktion f mit {{formula}}f(x)=0,2(x-1)(x+2)(x-4){{/formula}}.
39 39  Triff mindestens vier Aussagen über das Schaubild und begründe, weshalb diese ausreichen, um einen Ansatz für die Ermittlung eines Funktionsterms zu bestimmen.
40 40  [[image:Schaubild Aufgabe 1.png||width=40%]]
41 41  {{/aufgabe}}
42 42  
43 -{{aufgabe id="Fragestellungen zu einer Wertetabelle" afb="II" kompetenzen="K1, K4, K5, K6" quelle="Martina Wagner, Dirk Tebbe, Martin Rathgeb, Martin Stern" zeit="20" cc="by-sa"}}
44 -Gegeben ist der Ausschnitt einer Wertetabelle einer Funktion 3. Grades
45 -(% class="border slim" %)
46 -|{{formula}}x{{/formula}}|-4|-3,5|-3|-2,5|-2|-1,5|-1|-0,5|0
47 -|{{formula}}f(x){{/formula}}|-3|-0,625|0|-0,375|-1|-1,125|0|3,125|9
48 -
49 -(% class="abc" %)
50 -1. (((Begründe, dass folgende Aussagen wahr sind:
51 -1. Der Graph der Funktion f hat eine doppelte Nullstelle bei -3.
52 -1. Der Graph der Funktion f hat eine einfache Nullstelle bei -1.
53 -1. Der Graph verläuft vom dritten in den ersten Quadranten.
54 -1. Der Punkt R(1|-8) liegt nicht auf dem Graphen der Funktion f.
55 -
56 -)))
57 -1. Ermittle die Funktionsgleichung von f in der Produktform.
58 -{{/aufgabe}}
59 -
60 -{{aufgabe id="Bedingungen zum Aufstellen" afb="II" kompetenzen="K4, K5" quelle="Miriam Erdmann" zeit="7" cc="by-sa"}}
47 +{{aufgabe id="Aussagen über das Schaubild einer Funktion treffen" afb="II" kompetenzen="K4, K5" quelle="Miriam Erdmann" zeit="" cc="" }}
61 61  Gegeben sind die Schaubilder dreier Funktionen. Gib jeweils den Grad der zugehörigen Funktion sowie notwendige Bedingungen zum Aufstellen des Funktionsterms an.
62 - [[image:Bedingungen f.svg||width=30%]] [[image:Bedingungen g.svg||width=30%]] [[image:Bedingungen h.svg||width=30%]]
49 + [[image:Schaubild 1 Aufgabe 2.png||width=30%]] [[image:Schaubild 2 Aufgabe 2.png||width=30%]] [[image:Schaubild 3 Aufgabe 2.png||width=30%]]
63 63  {{/aufgabe}}
64 64  
65 -{{aufgabe id="Funktionstermbestimmung bei Polynomfunktionen" afb="II" kompetenzen="K4, K5" quelle="Niklas Wunder, Martin Stern" zeit="" cc="by-sa"}}
52 +{{aufgabe id="Funktionstermbestimmung bei Polynomfunktionen" afb="II" kompetenzen="K4, K5" quelle="Niklas Wunder, Martin Stern" zeit="" cc="" }}
66 66  Bestimme einen Funktionsterm einer Polynomfunktion mit den folgenden Eigenschaften:
67 67  a) Das Schaubild hat bei {{formula}}x=1{{/formula}} eine sechsfache Nullstelle und schneidet die y-Achse an der Stelle 4.
68 68  b) Das Schaubild hat bei {{formula}}x=-4{{/formula}} eine einfache, bei {{formula}}x=-2{{/formula}} eine doppelte und bei {{formula}}x=3{{/formula}} eine dreifache Nullstelle. Außerdem schneidet es die y-Achse bei {{formula}}y=27{{/formula}}.
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69 69  c) Das Schaubild ist symmetrisch zur y-Achse und geht durch {{formula}}P(2|10){{/formula}} und {{formula}}Q(0|0){{/formula}}.
70 70  d) Das Schaubild verläuft punktsymmetrisch zum Ursprung. Es hat eine einfache Nullstelle bei {{formula}}x=4{{/formula}} und eine doppelte Nullstelle bei {{formula}}x=-3{{/formula}}.
71 71  {{/aufgabe}}
72 -
73 -{{lehrende}}
74 -K3 wurde absichtlich weggelassen, weil das in 3.5 kommt. Für AFB III könnte man noch Aufgaben entwickeln. Vlt iwas mit Symmetrie und symmetrischen Nullstellen, die für die Aufstellung nicht geeignet sind, da sie redundante Information darstellen. Oder widersprüchliche Bedingungen, die eine Funktion nicht erfüllen kann.
75 -Schön wären auch noch Fragen nach dem mindestens erforderlichen Grad für einen Satz von Bedingungen, der Redundanzen enthält.
76 -{{/lehrende}}
77 -
78 -{{seitenreflexion bildungsplan="3" kompetenzen="4" anforderungsbereiche="4" kriterien="5" menge="2"}}
Bedingungen f.svg
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1 -XWiki.holgerengels
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