Änderungen von Dokument BPE 3.2 Funktionsgraph
Zuletzt geändert von Holger Engels am 2025/03/31 21:43
Von Version 45.4
bearbeitet von Holger Engels
am 2024/11/15 10:21
am 2024/11/15 10:21
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Auf Version 49.1
bearbeitet von Holger Engels
am 2024/11/15 15:04
am 2024/11/15 15:04
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... ... @@ -8,11 +8,11 @@ 8 8 [[Kompetenzen.K6.WebHome]] Ich kann die Eigenschaften einer Polynomfunktion mithilfe mathematischer Symbolsprache formulieren 9 9 [[Kompetenzen.K4.WebHome]] Ich kann das Schaubild mithilfe einer Wertetabelle zeichnen 10 10 11 -{{aufgabe id="Funktionsschaubild mit Hilfe einer Wertetabelle zeichnen" afb="I" kompetenzen="K4" quelle="Niklas Wunder, Martin Stern" cc="by-sa"}} 11 +{{aufgabe id="Funktionsschaubild mit Hilfe einer Wertetabelle zeichnen" afb="I" kompetenzen="K4" quelle="Niklas Wunder, Martin Stern" cc="by-sa" zeit="9"}} 12 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 13 {{/aufgabe}} 14 14 15 -{{aufgabe id="Symmetrie untersuchen" afb="II" kompetenzen="" quelle="Niklas Wunder" cc="by-sa"}} 15 +{{aufgabe id="Symmetrie untersuchen" afb="II" kompetenzen="" quelle="Niklas Wunder" cc="by-sa" zeit="10"}} 16 16 Untersuche die Graphen der Funktionen auf Symmetrie zum Koordinatenursprung und zur y-Achse. 17 17 (% style="list-style:alphastyle" %) 18 18 1. {{formula}}f(x)=3\,x+1{{/formula}} ... ... @@ -23,38 +23,37 @@ 23 23 1. {{formula}}f(x)=x^4\,(x^3-3)\cdot (1-x){{/formula}} 24 24 {{/aufgabe}} 25 25 26 -{{aufgabe id="Symmetrie Parameter bestimmen" afb="III" kompetenzen="" quelle="Niklas Wunder" cc="by-sa"}} 27 -Bestimme einen Zahlenwert {{formula}} 28 -a) {{formula}} 29 -b) {{formula}} 30 -c) {{formula}} 31 -d) {{formula}} 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 32 {{/aufgabe}} 33 33 34 -{{aufgabe id="Globalverlauf untersuchen" afb="I" kompetenzen="" quelle="Niklas Wunder, Martin Stern" cc="by-sa"}} 34 +{{aufgabe id="Globalverlauf untersuchen" afb="I" kompetenzen="" quelle="Niklas Wunder, Martin Stern" cc="by-sa" zeit="4"}} 35 35 Untersuche das Verhalten der Funktion {{formula}}f{{/formula}} für {{formula}}x\rightarrow\pm \infty{{/formula}}: 36 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}} //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 41 {{/aufgabe}} 42 42 43 -{{aufgabe id="Schnittpunkte mit den Koordinatenachsen bestimmen" afb="I" kompetenzen="" quelle="Niklas Wunder, Martin Stern" cc="by-sa"}} 44 -Bestimme alle Schnittpunkte des Graphen der Funktion {{formula}}f{{/formula}} mit den Koordinatenachsen: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 45 (% style="list-style:alphastyle" %) 46 -1. {{formula}}f(x)=\frac{3}{4}x+2{{/formula}} // 47 -1. {{formula}}f(x)=(x-2)^4-1{{/formula}} // 48 -1. {{formula}}f(x)=2\cdot(x-3)\cdot(x+4)\cdot(x-2){{/formula}} // 49 -1. {{formula}}f(x)=3\cdot(x-9)\cdot(x^2-4){{/formula}} // 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}} 50 50 {{/aufgabe}} 51 51 52 -{{aufgabe id="Funktionsgraph mit Nullstellen skizzieren" afb="I" kompetenzen="" quelle="Niklas Wunder, Martin Stern" cc="by-sa"}} 53 -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 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 54 54 (% style="list-style:alphastyle" %) 55 -1. {{formula}}f_1(x)=(x-2)^2{{/formula}} //56 -1. {{formula}}f_2(x)=(x+2)^3{{/formula}} //57 -1. {{formula}}f_3(x)=(x-2)\cdot(x-3)\cdot x^2{{/formula}} //58 -1. {{formula}}f_4(x)=-\frac{1}{10}(x^2-9)\cdot x^3{{/formula}} //59 -1. {{formula}}f_5(x)= \frac{1}{4}(x-2)^2\cdot(x+2)^2-1{{/formula}}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}} 60 60 {{/aufgabe}}
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... ... @@ -1,1 +1,1 @@ 1 -Aufgabe "Schnittpunkte mit den Koordinatenachsen bestimmen" überarbeiten. 1 +Lösung zu Aufgabe "Schnittpunkte mit den Koordinatenachsen bestimmen" überarbeiten.
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... ... @@ -1,0 +1,1 @@ 1 +XWiki.holgerengels - Kommentar
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... ... @@ -1,0 +1,1 @@ 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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... ... @@ -1,0 +1,1 @@ 1 +2024-11-15 10:37:19.20
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... ... @@ -1,0 +1,1 @@ 1 +XWiki.holgerengels - Kommentar
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... ... @@ -1,0 +1,1 @@ 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]]) - Datum
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... ... @@ -1,0 +1,1 @@ 1 +2024-11-15 11:17:25.685