Änderungen von Dokument Lösung Bedingungen zum Aufstellen

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4	4	Die Schaubilder {{formula}}K_f{{/formula}} und {{formula}}K_g{{/formula}} haben Grad 3, das Schaubild {{formula}}K_h{{/formula}} Grad 4. Dementsprechend benötigt man für den ersten und letzten Funktionsterm vier, für den zweiten fünf bzw. drei Bedingungen.
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6		-Schaubild 1: Funktion dritten Grades, hat die drei einfachen Nullstellen {{formula}}x_1=-2{{/formula}}, {{formula}}x_2=1{{/formula}} und {{formula}}x_3=4{{/formula}} und schneidet die y-Achse bei {{formula}}y=2{{/formula}} (Ansatz mit Produktform).
7		-Schaubild 2: Funktion vierten Grades und achsensymmetrisch: benötigt nur noch drei Bedingungen. Mit den Punkten {{formula}} A(-2|2), B(0|2){{/formula}} und {{formula}}C(2|2){{/formula}}, die sich zunächst aufdrängen, kann man nicht arbeiten. //A// und //C// sind redundant aufgrund der Symmetrie. Setzt man beide an, erhält man zweimal die gleiche Gleichung. Dazu kommt, dass die Punkte //A//, //B//, //C// alle den gleichen Funktionswert aufweisen. Damit kann man kein //a// bestimmen. Wenn man statt //C// den Punkt {{formula}}D(1|-1){{/formula}} nimmt, kommt man zum Ziel.
	6	+**Schaubild 1:** Funktion dritten Grades, hat die drei einfachen Nullstellen {{formula}}x_1=-2{{/formula}}, {{formula}}x_2=1{{/formula}} und {{formula}}x_3=4{{/formula}} und schneidet die y-Achse bei {{formula}}y=2{{/formula}} (Ansatz mit Produktform).
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	8	+**Schaubild 2:** Funktion vierten Grades und achsensymmetrisch: benötigt nur noch drei Bedingungen. Mit den Punkten {{formula}} A(-2|2), B(0|2){{/formula}} und {{formula}}C(2|2){{/formula}}, die sich zunächst aufdrängen, kann man nicht arbeiten. //A// und //C// sind redundant aufgrund der Symmetrie. Setzt man beide an, erhält man zweimal die gleiche Gleichung. Dazu kommt, dass die Punkte //A//, //B//, //C// alle den gleichen Funktionswert aufweisen. Damit kann man kein //a// bestimmen. Wenn man statt //C// den Punkt {{formula}}D(1|-1){{/formula}} nimmt, kommt man zum Ziel.
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9	9	Man kann hier übrigens alternativ eine Funktion {{formula}}g(x){{/formula}} mit Produktform ansetzen, die sich durch vertikale Verschiebung des Graphen um zwei nach unten ergibt. Durch anschließende Verschiebung um zwei nach oben, erhält man den Funktionsterm zum Schaubild.
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11		-Schaubild 3: Funktion dritten Grades: benötigt vier Bedingungen, z.B.: {{formula}} A(-1|-3), B(0|1), C(1|-1){{/formula}} und {{formula}}D(2|-3){{/formula}}
	12	+**Schaubild 3:** Funktion dritten Grades: benötigt vier Bedingungen, z.B.: {{formula}} A(-1|-3), B(0|1), C(1|-1){{/formula}} und {{formula}}D(2|-3){{/formula}}
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13	13	Auch hier kann man alternativ mit Verschiebung arbeiten.

Bedingungen g.svg

Author

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	1	+XWiki.holgerengels

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