Änderungen von Dokument BPE 3.3 Aufstellen von Funktionstermen
Zuletzt geändert von Martin Rathgeb am 2025/04/06 23:13
Von Version 1.1
bearbeitet von holger
am 2022/11/13 17:58
am 2022/11/13 17:58
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Auf Version 70.1
bearbeitet von Holger Engels
am 2024/11/22 09:02
am 2024/11/22 09:02
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Zusammenfassung
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... ... @@ -1,1 +1,1 @@ 1 -Aufstellen von Funktionstermen 1 +BPE 3.3 Aufstellen von Funktionstermen - Übergeordnete Seite
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... ... @@ -1,1 +1,1 @@ 1 - Main.WebHome1 +Eingangsklasse.WebHome - Dokument-Autor
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... ... @@ -1,1 +1,1 @@ 1 -XWiki.holger 1 +XWiki.holgerengels - Inhalt
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... ... @@ -2,6 +2,57 @@ 2 2 {{toc start=2 depth=2 /}} 3 3 {{/box}} 4 4 5 - DieSchülerinnen und Schüler bestimmen aus grafisch,tabellarisch oder verbal gegebenen Funktionseigenschaften einen geeigneten Ansatzund Bedingungen,die zur Ermittlung des Funktionsterms dienen. Ebenso ermitteln sie in geeigneten Fällen den Funktionsterm.5 +=== Kompetenzen === 6 6 7 +[[Kompetenzen.K5]] Ich kann den passenden Ansatz für die Ermittlung eines Funktionsterms anhand gegebener Bedingungen bestimmen 8 +[[Kompetenzen.K4]] [[Kompetenzen.K5]] Ich kann den Funktionsterm anhand verbal gegebener Bedingungen aufstellen 9 +[[Kompetenzen.K4]] [[Kompetenzen.K5]] Ich kann den Funktionsterm anhand tabellarisch gegebener Bedingungen aufstellen 10 +[[Kompetenzen.K4]] [[Kompetenzen.K5]] Ich kann den Funktionsterm anhand eines Schaubilds aufstellen 7 7 12 +{{aufgabe id="Änderungen sind bemerkenswert" afb="I" kompetenzen="K2, K4, K5" quelle="Martin Rathgeb, Martin Stern" zeit="" cc="" }} 13 +(% class="border slim" %) 14 +Liegen die Punkte auf einer Parabel? 15 +(% class="border slim" %) 16 +|{{formula}}x{{/formula}}|0|1|2 17 +|{{formula}}f_1(x){{/formula}}|1|1|1 18 +|{{formula}}f_2(x){{/formula}}|1|3|5 19 +{{/aufgabe}} 20 + 21 +{{aufgabe id="Parabel aus zwei Punktproben mit Zusatzinformation" afb="II" kompetenzen="K2, K4, K5" quelle="Martin Rathgeb, Martin Stern" zeit="" cc="" }} 22 +//Scheitel(punkts)form.// Bestimme aus folgenden Wertetabellen (je zwei Wertepaare) mit Zusatzinformation jeweils die quadratische Funktion. 23 +(% class="border slim" %) 24 +|{{formula}}x{{/formula}}|1|3| 25 +|{{formula}}f_1(x){{/formula}}|2|1|{{formula}}x_s=3{{/formula}} 26 +|{{formula}}f_2(x){{/formula}}|0|0|{{formula}}y_s=2{{/formula}} 27 +|{{formula}}f_3(x){{/formula}}|2|2|{{formula}}y_s=4{{/formula}} 28 +|{{formula}}f_4(x){{/formula}}|2|1|{{formula}}y_s=2{{/formula}} 29 +{{/aufgabe}} 30 + 31 +{{aufgabe id="Parabel aus drei Punktproben" afb="II" kompetenzen="K2, K4, K5" quelle="Martin Rathgeb, Martin Stern" zeit="" cc="" }} 32 +//Haupt-, Scheitel(punkts)-, Produktform.// Bestimme aus folgenden Wertetabellen (je drei Wertepaare) jeweils die quadratische Funktion. 33 +(% class="border slim" %) 34 +|{{formula}}x{{/formula}}|1|2|3 35 +|{{formula}}f_1(x){{/formula}}|0|0|1 36 +|{{formula}}f_2(x){{/formula}}|3|1|3 37 +|{{formula}}f_3(x){{/formula}}|-2|1|2 38 +|{{formula}}f_4(x){{/formula}}|-2|0|-2 39 +{{/aufgabe}} 40 + 41 +{{aufgabe id="Produktdarstellung" afb="I" kompetenzen="K4, K5" quelle="Miriam Erdmann" zeit="5" cc="" }} 42 +Gegeben ist das Schaubild der Funktion f mit {{formula}}f(x)=0,2(x-1)(x+2)(x-4){{/formula}}. 43 +Triff mindestens vier Aussagen über das Schaubild und begründe, weshalb diese ausreichen, um einen Ansatz für die Ermittlung eines Funktionsterms zu bestimmen. 44 +[[image:Schaubild Aufgabe 1.png||width=40%]] 45 +{{/aufgabe}} 46 + 47 +{{aufgabe id="Aussagen über das Schaubild einer Funktion treffen" afb="II" kompetenzen="K4, K5" quelle="Miriam Erdmann" zeit="" cc="" }} 48 +Gegeben sind die Schaubilder dreier Funktionen. Gib jeweils den Grad der zugehörigen Funktion sowie notwendige Bedingungen zum Aufstellen des Funktionsterms an. 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%]] 50 +{{/aufgabe}} 51 + 52 +{{aufgabe id="Funktionstermbestimmung bei Polynomfunktionen" afb="II" kompetenzen="K4, K5" quelle="Niklas Wunder, Martin Stern" zeit="" cc="" }} 53 +Bestimme einen Funktionsterm einer Polynomfunktion mit den folgenden Eigenschaften: 54 +a) Das Schaubild hat bei {{formula}}x=1{{/formula}} eine sechsfache Nullstelle und schneidet die y-Achse an der Stelle 4. 55 +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}}. 56 +c) Das Schaubild ist symmetrisch zur y-Achse und geht durch {{formula}}P(2|10){{/formula}} und {{formula}}Q(0|0){{/formula}}. 57 +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}}. 58 +{{/aufgabe}}
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