Änderungen von Dokument BPE 2.1 Funktionstypen und deren Eigenschaften
Zuletzt geändert von Holger Engels am 2025/03/31 21:42
Von Version 38.1
bearbeitet von Holger Engels
am 2024/10/14 12:10
am 2024/10/14 12:10
Änderungskommentar:
Neues Bild Stetigkeit ee.svg hochladen
Auf Version 17.1
bearbeitet von Holger Engels
am 2024/09/27 20:22
am 2024/09/27 20:22
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Zusammenfassung
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... ... @@ -5,50 +5,24 @@ 5 5 [[Kompetenzen.K1]] [[Kompetenzen.K4]] Ich kann die Eigenschaften von Potenzfunktionen ausgehend von den Funktionsgraphen erläutern 6 6 [[Kompetenzen.K1]] Ich kann den Stetigkeitsbegriff anschaulich anhand der Graphen von Potenzfunktionen erläutern 7 7 8 -Verhalten +/- oo 9 -Verhalten nahe Definitionslücke 10 -Asymptoten 11 -Symmetrie 12 -Stetigkeit 8 +Zuordnen, Skizzieren 13 13 14 -{{aufgabe id="Skizzieren" afb="I" kompetenzen="" quelle="Holger Engels" cc="BY-SA"}} 15 -Skizziere die Graphen der Funktionen //f// und //g// mit {{formula}}f(x)=x^3{{/formula}} und {{formula}}g(x) = x^{1/3}{{/formula}} in ein gemeinsames Koordinatensystem, dessen x- und y-Achse jeweils von {{formula}}[-8; +8]{{/formula}} geht. 16 -{{/aufgabe}} 10 +definiert auf ganz R 11 +symmetrisch zum ursprung 12 +P(1|1) € Gf 13 +f(x) -> +oo für x -> +oo 17 17 18 -{{aufgabe id="D und W" afb="I" kompetenzen="" quelle="Holger Engels" cc="BY-SA"}} 19 -Gib jeweils den Definitions- und den Wertebereich an: 20 -1. {{formula}}f(x)=\frac{1}{x-2}+1{{/formula}} 21 -1. {{formula}}g(x)=\sqrt{x+2}-1{{/formula}} 22 -{{/aufgabe}} 23 - 24 24 {{aufgabe id="Eigenschaften" afb="I" kompetenzen="K1, K5" quelle="??" cc="BY-SA"}} 25 -Bestimme zu den unten genannten Funktionen den (1) Globalverlauf, die (2) Symmetrie, den (3) Definitions- und den (4) Wertebereich und gegebenenfalls (5) waagerechte und senkrechte Asymptoten. 16 +Bestimmen Sie zu den unten genannten Funktionen den (1) Globalverlauf, die (2) Symmetrie, den (3) Definitions- und den (4) Wertebereich und gegebenenfalls (5) waagerechte und senkrechte Asymptoten. 26 26 27 -(% style="list-style: alphastyle" %) 28 -1. Das Schaubild der Funktion g ist eine Parabel vierter Ordnung mit dem Scheitel {{formula}}S(-2| 3){{/formula}}, die um den Streckungsfaktor {{formula}}\frac{1}{2}{{/formula}} in y-Richtung gestreckt wurde. 29 -1. Die Funktion h ist eine Potenzfunktion mit {{formula}}h(x) = \frac{-3}{x-2}+4{{/formula}} 18 +a) Das Schaubild der Funktion g ist eine Parabel vierter Ordnung mit dem Scheitel {{formula}}S(-2| 3){{/formula}}, die um den Streckungsfaktor {{formula}}\frac{1}{2} {{/formula}} in y-Richtung gestreckt wurde. 19 +b) Die Funktion h ist eine Potenzfunktion mit {{formula}}h(x) = \frac{-3}{(x-2)} +4 {{/formula}} 30 30 {{/aufgabe}} 31 31 32 -{{aufgabe id="Venn - Eigenschaften" afb="II" kompetenzen="K2, K4, K5" quelle="Holger Engels" cc="BY-SA" zeit="8" tags="problemlösen"}} 33 -[[image:venn.svg|| width="500" style="float: left"]] 34 -Gib für jedes Feld **A** .. **H** eine passende Funktion {{formula}}f(x)=a\cdot x^n{{/formula}} an. Sollte ein Feld nicht gefüllt werden können, begründe bitte, warum es nicht geht. 35 - 36 -(% style="width: calc(100% - 500px); min-width: 300px" %) 37 -|= A | 38 -|= B | 39 -|= C | 40 -|= D | 41 -|= E | 42 -|= F | 43 -|= G | 44 -|= H | 45 - 46 -**Zusatzaufgabe:** Finde möglichst einfache/ komplexe Lösungen. 22 +{{aufgabe id="Venn" afb="II" kompetenzen="" quelle="Holger Engels" cc="BY-SA"}} 23 +[[image:venn.svg]] 47 47 {{/aufgabe}} 48 48 49 -{{aufgabe id="Stetigkeit" afb="II" kompetenzen="" quelle="Martin Rathgeb, Holger Engels" cc="BY-SA" zeit="5"}} 50 -Sascha behauptet, die Funktion //f// mit {{formula}}f(x) = \frac{1}{x}{{/formula}} sei auf ihrem maximalen Definitionsbereich nicht stetig, weil man ihren Graphen nicht ohne Absetzen zeichnen kann. Nimm dazu Stellung! 51 -{{/aufgabe}} 52 52 53 53 54 54
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... ... @@ -1,1 +1,0 @@ 1 -XWiki.holgerengels - Größe
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... ... @@ -1,1 +1,0 @@ 1 -XWiki.holgerengels - Größe
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... ... @@ -1,1 +1,0 @@ 1 -XWiki.holgerengels - Größe
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