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Änderungen von Dokument Lösung Bedingungen zum Aufstellen

Zuletzt geändert von Holger Engels am 2025/03/30 13:49
Von Version 19.1
bearbeitet von Holger Engels
am 2025/03/30 13:45
Änderungskommentar: Neues Bild Bedingungen h.svg hochladen
Auf Version 21.2
bearbeitet von Holger Engels
am 2025/03/30 13:49
Änderungskommentar: Es gibt keinen Kommentar für diese Version

Zusammenfassung

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3 3  
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.
5 5  
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).
8 8  
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.
9 +
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.
10 10  
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}}
12 12  
13 13  Auch hier kann man alternativ mit Verschiebung arbeiten.
Bedingungen f.svg
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1 +XWiki.holgerengels
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