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Änderungen von Dokument BPE 3.2 Funktionsgraph

Zuletzt geändert von Holger Engels am 2025/03/31 21:43
Von Version 60.1
bearbeitet von Holger Engels
am 2024/11/17 19:35
Änderungskommentar: Neues Bild Fertig zeichnen.svg hochladen
Auf Version 48.1
bearbeitet von Holger Engels
am 2024/11/15 15:04
Änderungskommentar: Neues Bild Fertig zeichnen.svg hochladen

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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="Punkte" afb="I" kompetenzen="K4" quelle="Stefanie Schmidt" cc="by-sa" zeit="2"}}
16 -Das Schaubild einer Funktion, die punktsymmetrisch zum Ursprung ist, enthält die Punkte {{formula}}P_1(1|-2){{/formula}} und {{formula}}P_2(-3|4){{/formula}}. Nenne drei weitere Punkte, die auf dem Schaubild liegen.
17 -{{/aufgabe}}
18 -
19 -{{aufgabe id="Symmetrie untersuchen" afb="I" kompetenzen="K4,K5" quelle="Niklas Wunder" cc="by-sa" zeit="10"}}
15 +{{aufgabe id="Symmetrie untersuchen" afb="II" kompetenzen="" quelle="Niklas Wunder" cc="by-sa" zeit="10"}}
20 20  Untersuche die Graphen der Funktionen auf Symmetrie zum Koordinatenursprung und zur y-Achse.
21 21  (% style="list-style:alphastyle" %)
22 22  1. {{formula}}f(x)=3\,x+1{{/formula}}
... ... @@ -27,8 +27,8 @@
27 27  1. {{formula}}f(x)=x^4\,(x^3-3)\cdot (1-x){{/formula}}
28 28  {{/aufgabe}}
29 29  
30 -{{aufgabe id="Symmetrie Parameter bestimmen" afb="II" kompetenzen="K5" quelle="Niklas Wunder" cc="by-sa" zeit="8"}}
31 -Bestimme einen Zahlenwert {{formula}}a{{/formula}} so, dass der Graph symmetrisch zum Koordinatenursprung oder zur y- Achse ist.
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.
32 32  a) {{formula}}f(x)=x+a{{/formula}}
33 33  b) {{formula}}f(x)=(x+1)\cdot (x-a){{/formula}}
34 34  c) {{formula}}f(x)=x\cdot (x+a)^2{{/formula}}
... ... @@ -35,7 +35,7 @@
35 35  d) {{formula}}f(x)=x\cdot (x^2+a){{/formula}}
36 36  {{/aufgabe}}
37 37  
38 -{{aufgabe id="Globalverlauf untersuchen" afb="I" kompetenzen="K5,K6" quelle="Niklas Wunder, Martin Stern" cc="by-sa" zeit="4"}}
34 +{{aufgabe id="Globalverlauf untersuchen" afb="I" kompetenzen="" quelle="Niklas Wunder, Martin Stern" cc="by-sa" zeit="4"}}
39 39  Untersuche das Verhalten der Funktion {{formula}}f{{/formula}} für {{formula}}x\rightarrow\pm \infty{{/formula}}:
40 40  (% style="list-style:alphastyle" %)
41 41  1. {{formula}}f(x)=-x^3{{/formula}}
... ... @@ -44,7 +44,7 @@
44 44  1. {{formula}}f(x)=x\cdot(x+7)\cdot(x-7){{/formula}}
45 45  {{/aufgabe}}
46 46  
47 -{{aufgabe id="Schnittpunkte mit den Koordinatenachsen bestimmen" afb="I" kompetenzen="K4,K5" quelle="Niklas Wunder, Martin Stern" cc="by-sa" zeit="5"}}
43 +{{aufgabe id="Schnittpunkte mit den Koordinatenachsen bestimmen" afb="I" kompetenzen="" quelle="Niklas Wunder, Martin Stern" cc="by-sa" zeit="5"}}
48 48  Bestimme jeweils die Schnittpunkte mit ihren Vielfachheiten des Graphen der Funktion {{formula}}f{{/formula}} mit den Koordinatenachsen:
49 49  (% style="list-style:alphastyle" %)
50 50  1. {{formula}}f(x)=-2(x-\frac{3}{2}){{/formula}}
... ... @@ -52,21 +52,12 @@
52 52  1. {{formula}}f(x)=2\cdot(x-3)^3\cdot(x^2-4){{/formula}}
53 53  {{/aufgabe}}
54 54  
55 -{{aufgabe id="Funktionsgraph mit Nullstellen skizzieren" afb="I" kompetenzen="K4,K5" quelle="Niklas Wunder, Martin Stern" cc="by-sa" zeit="10"}}
56 -Gib die Nullstellen mit ihrer Vielfachheit an und skizziere anschließend den Graphen in einem geeigneten Intervall.
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
57 57  (% style="list-style:alphastyle" %)
58 58  1. {{formula}}f_1(x)=(x-2)^2{{/formula}}
59 59  1. {{formula}}f_2(x)=(x+2)^3{{/formula}}
60 60  1. {{formula}}f_3(x)=(x-2)\cdot(x-3)\cdot x^2{{/formula}}
61 -1. {{formula}}f_4(x)=-\frac{1}{10}(x^2-9)\cdot (x-3){{/formula}}
57 +1. {{formula}}f_4(x)=-\frac{1}{10}(x^2-9)\cdot x^3{{/formula}}
62 62  1. {{formula}}f_5(x) = (x-3)^5{{/formula}}
63 63  {{/aufgabe}}
64 -
65 -{{aufgabe id="Fertig zeichnen" afb="I" kompetenzen="K4" quelle="Stefanie Schmidt" cc="by-sa" zeit="3"}}
66 -Ergänze das Schaubild der Funktion //f// mit {{formula}}f(x)=\frac{1}{11,66}(x^7-8x^5+16x^3){{/formula}} im Intervall {{formula}}[0;2,5]{{/formula}}.
67 -[[image:Fertig zeichnen.svg]]
68 -{{/aufgabe}}
69 -
70 -{{lehrende}}K3 wurde bewusst weggelassen .. das kommt in BPE 3.5{{/lehrende}}
71 -
72 -{{seitenreflexion bildungsplan="5" kompetenzen="3" anforderungsbereiche="2" kriterien="3" menge="3"/}}
Fertig zeichnen.ggb
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1 -XWiki.holgerengels
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Fertig zeichnen.svg
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