Änderungen von Dokument BPE 3.2 Funktionsgraph

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  • Fertig zeichnen.ggb
  • Fertig zeichnen.svg
  • Polynomzeichnen1.png
  • Polynomzeichnen2.png
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Seiteneigenschaften

Titel

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1		-Funktionsgraph
	1	+BPE 3.2 Funktionsgraph

Übergeordnete Seite

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1		-Main.WebHome
	1	+Eingangsklasse.WebHome

Dokument-Autor

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1		-XWiki.holger
	1	+XWiki.holgerengels

Inhalt

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1		-{{box cssClass="floatinginfobox" title="**Contents**"}}
2		-{{toc start=2 depth=2 /}}
3		-{{/box}}
	1	+{{seiteninhalt/}}
4	4
5		-Die Schülerinnen und Schüler ermitteln die Eigenschaften von Polynomfunktionen ausgehend von den Funktionstermen und skizzieren die Funktionsgraphen. Sie geben die Eigenschaften auch mit mathematischer Symbolsprache an. Darüber hinaus zeichnen die Schülerinnen und Schüler einen Funktionsgraphen mithilfe einer
6		-Wertetabelle.
	3	+[[Kompetenzen.K4.WebHome]] Ich kann den Verlauf einer Polynomfunktion basierend auf dem Funktionsterm ermitteln
	4	+[[Kompetenzen.K4.WebHome]] [[Kompetenzen.K6]] Ich kann den Verlauf mit mathematischer Symbolsprache formulieren
	5	+[[Kompetenzen.K1.WebHome]] Ich kann Symmetrien aus dem Funktionsterm ermitteln
	6	+[[Kompetenzen.K6.WebHome]] [[Kompetenzen.K4]] Ich kann Symmetrien mit mathematischer Symbolsprache formulieren
	7	+[[Kompetenzen.K4.WebHome]] Ich kann das Schaubild zu einem gegebenen Funktionsterm skizzieren
	8	+[[Kompetenzen.K6.WebHome]] Ich kann die Eigenschaften einer Polynomfunktion mithilfe mathematischer Symbolsprache formulieren
	9	+[[Kompetenzen.K4.WebHome]] Ich kann das Schaubild mithilfe einer Wertetabelle zeichnen
	10	+
	11	+{{aufgabe id="Funktionsschaubild mit Hilfe einer Wertetabelle zeichnen" afb="I" kompetenzen="K4" quelle="Niklas Wunder, Martin Stern" cc="by-sa" zeit="9"}}
	12	+Zeichne das Schaubild der Funktion {{formula}}f(x)=-0,5x^4+0,7x^3+2x^2-1{{/formula}} mit Hilfe einer Wertetabelle für {{formula}}-2\leq x\leq 3{{/formula}} in ein geeignetes Koordinatensystem ein.
	13	+{{/aufgabe}}
	14	+
	15	+{{aufgabe id="Symmetrie untersuchen" afb="II" kompetenzen="" quelle="Niklas Wunder" cc="by-sa" zeit="10"}}
	16	+Untersuche die Graphen der Funktionen auf Symmetrie zum Koordinatenursprung und zur y-Achse.
	17	+(% style="list-style:alphastyle" %)
	18	+1. {{formula}}f(x)=3\,x+1{{/formula}}
	19	+1. {{formula}}f(x)=7{{/formula}}
	20	+1. {{formula}}f(x)=4\,x^3-8\,x+2{{/formula}}
	21	+1. {{formula}}f(x)=-2\,x^4-9\,x^2+3{{/formula}}
	22	+1. {{formula}}f(x)=(x^2-2)^3{{/formula}}
	23	+1. {{formula}}f(x)=x^4\,(x^3-3)\cdot (1-x){{/formula}}
	24	+{{/aufgabe}}
	25	+
	26	+{{aufgabe id="Symmetrie Parameter bestimmen" afb="III" kompetenzen="" quelle="Niklas Wunder" cc="by-sa" zeit="8"}}
	27	+Bestimme einen Zahlenwert {{formula}}a{{/formula}} so, dass der Graph symmetrisch zum Koordinatenursprung oder zur y- Achse ist.
	28	+a) {{formula}}f(x)=x+a{{/formula}}
	29	+b) {{formula}}f(x)=(x+1)\cdot (x-a){{/formula}}
	30	+c) {{formula}}f(x)=x\cdot (x+a)^2{{/formula}}
	31	+d) {{formula}}f(x)=x\cdot (x^2+a){{/formula}}
	32	+{{/aufgabe}}
	33	+
	34	+{{aufgabe id="Globalverlauf untersuchen" afb="I" kompetenzen="" quelle="Niklas Wunder, Martin Stern" cc="by-sa" zeit="4"}}
	35	+Untersuche das Verhalten der Funktion {{formula}}f{{/formula}} für {{formula}}x\rightarrow\pm \infty{{/formula}}:
	36	+(% style="list-style:alphastyle" %)
	37	+1. {{formula}}f(x)=-x^3{{/formula}}
	38	+1. {{formula}}f(x)=2x^4+3x^3-7x^2+x{{/formula}}
	39	+1. {{formula}}f(x)=x^3+100x^2-0,01x^6+1000{{/formula}}
	40	+1. {{formula}}f(x)=x\cdot(x+7)\cdot(x-7){{/formula}}
	41	+{{/aufgabe}}
	42	+
	43	+{{aufgabe id="Schnittpunkte mit den Koordinatenachsen bestimmen" afb="I" kompetenzen="" quelle="Niklas Wunder, Martin Stern" cc="by-sa" zeit="5"}}
	44	+Bestimme jeweils die Schnittpunkte mit ihren Vielfachheiten des Graphen der Funktion {{formula}}f{{/formula}} mit den Koordinatenachsen:
	45	+(% style="list-style:alphastyle" %)
	46	+1. {{formula}}f(x)=-2(x-\frac{3}{2}){{/formula}}
	47	+1. {{formula}}f(x)=2\cdot(x-3)^2\cdot(x+2)\cdot(x-2){{/formula}}
	48	+1. {{formula}}f(x)=2\cdot(x-3)^3\cdot(x^2-4){{/formula}}
	49	+{{/aufgabe}}
	50	+
	51	+{{aufgabe id="Funktionsgraph mit Nullstellen skizzieren" afb="I" kompetenzen="" quelle="Niklas Wunder, Martin Stern" cc="by-sa" zeit="10"}}
	52	+Gib die Nullstellen mit ihrer Vielfachheit an und skizziere anschließend den Graphen in einem geeigneten Intervall. Hinweis: Bei der e) gebe die Stellen mit {{formula}}f(x)=-1{{/formula}} an
	53	+(% style="list-style:alphastyle" %)
	54	+1. {{formula}}f_1(x)=(x-2)^2{{/formula}}
	55	+1. {{formula}}f_2(x)=(x+2)^3{{/formula}}
	56	+1. {{formula}}f_3(x)=(x-2)\cdot(x-3)\cdot x^2{{/formula}}
	57	+1. {{formula}}f_4(x)=-\frac{1}{10}(x^2-9)\cdot x^3{{/formula}}
	58	+1. {{formula}}f_5(x) = (x-3)^5{{/formula}}
	59	+{{/aufgabe}}
	60	+
	61	+{{aufgabe id="Fertig zeichnen" afb="I" kompetenzen="" quelle="Stefanie Schmidt" cc="by-sa" zeit="3"}}
	62	+Ergänze das Schaubild der Funktion //f// mit {{formula}}f(x)=\frac{1}{1,1}x^3(x+2)^2{{/formula}} im Intervall {{formula}}[0;2,5]{{/formula}}.
	63	+[[image:Fertig zeichnen.svg]]
	64	+{{/aufgabe}}

Fertig zeichnen.ggb

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	1	+XWiki.niklaswunder

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	1	+XWiki.niklaswunder

Größe

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Inhalt

XWiki.XWikiComments[0]

Autor

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	1	+XWiki.holgerengels

Kommentar

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	1	+Lösung zu Aufgabe "Schnittpunkte mit den Koordinatenachsen bestimmen" überarbeiten.

Datum

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	1	+2024-11-15 10:11:17.638

XWiki.XWikiComments[1]

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	1	+XWiki.holgerengels

Kommentar

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	1	+Man könnte noch eine Aufgabe dazu machen, die zeigt, dass die Symmetrie in der Hauptform auch feststellbar ist, wenn die Summanden entweder alle gerade oder alle ungerade Potenzfunktionen sind.

Datum

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	1	+2024-11-15 10:37:19.20

XWiki.XWikiComments[2]

Autor

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	1	+XWiki.holgerengels

Kommentar

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	1	+Eine Aufgabe, die zeigt, warum der Summand mit der höchsten Potenz den Verlauf bestimmt (so etwa [[KMap>>https://kmap.eu/app/browser/Mathematik/Ganzrationale%20Funktionen/Verlauf#beispiel-----verhalten-im-unendlichen]])

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	1	+2024-11-15 11:17:25.685