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Zuletzt geändert von Holger Engels am 2025/03/11 21:51
Von Version 66.5
bearbeitet von Holger Engels
am 2025/02/25 12:28
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Auf Version 69.1
bearbeitet von Holger Engels
am 2025/02/25 15:53
Änderungskommentar: Neues Bild graph f.svg hochladen

Zusammenfassung

Details

Seiteneigenschaften
Inhalt
... ... @@ -9,13 +9,18 @@
9 9  {{lehrende}}
10 10  x im Exponenten
11 11  * Welches ist eine Exponentialfunktion, welches nicht? Ordne zu ... (komplexere Terme mit/ ohne x im Exponenten)
12 +
12 12  Asymptotischer Verlauf
13 -* Schaubilder von tan(x), 1/100 x^2 und x^-2 .. jeweils Ausschnitte
14 -* 2^x und 2^-x = ½^x
14 +* Schaubilder , die durch (0|1) verlaufen
15 +* 1, 1 + 2x, 1 + x^2, 2^x, 1/2^x .. 1/x^2 für x<0 weiterzeichnen
16 +* Funktionswert an den Stellen -1, 0, 1, 2
17 +
15 15  Warum kommen nur positive Basen in Frage?
16 16  * Wertetabelle (-2)^x
17 -Basiswechsel (setzt ln voraus)
18 -* Potenzgesetz
20 +
21 +Basiswechsel
22 +* ohne ln
23 +* Auf Potenzgesetz zurückführen
19 19  {{/lehrende}}
20 20  
21 21  {{lernende}}
... ... @@ -22,6 +22,20 @@
22 22  [[GeoGebra-Buch>>https://www.geogebra.org/m/khnsgz5a#material/UcgSUN2M]]
23 23  {{/lernende}}
24 24  
30 +{{aufgabe id="Exponentialfunktion" afb="I" kompetenzen="K5" quelle="Holger Engels" zeit="2"}}
31 +Entscheide jeweils, ob es sich bei dem Funktionsterm um einen Exponentialfunktionsterm handelt.
32 +(% class="abc" %)
33 +1. {{formula}}f(x) = \frac{1}{8}(2(x-2))^3 + e{{/formula}}
34 +1. {{formula}}f(x) = \frac{1}{8}x^{3(x+1)}-1{{/formula}}
35 +{{/aufgabe}}
36 +
37 +{{aufgabe id="Graphen" afb="I" kompetenzen="K4" quelle="Holger Engels" zeit="8"}}
38 +Ordne die Funktionsgraphen den Funktionstermen zu und skizziere jeweils im Schaubild den Abschnitt für //x<0//.
39 +{{formula}}f(x)=1+2x{{/formula}} {{formula}}g(x)=1 + x^2{{/formula}} {{formula}}h(x)=(\frac{1}{2})^x{{/formula}} {{formula}}\frac{1}{(x+1)^2}{{/formula}}{{formula}}i(x)=2^x{{/formula}}
40 +[[image:graph f.svg||style="margin: 8px"]] [[image:graph g.svg||style="margin: 8px"]] [[image:graph h.svg||style="margin: 8px"]] [[image:graph p.svg||style="margin: 8px"]] [[image:graph q.svg||style="margin: 8px"]] [[image:graph r.svg||style="margin: 8px"]]
41 +(% class="abc" %)
42 +{{/aufgabe}}
43 +
25 25  {{aufgabe id="Basiswechel" afb="I" kompetenzen="K4" quelle="Niklas Wunder, Katharina Schneider" zeit="10"}}
26 26  Wandle die gegeben Exponentialfunktion in die entsprechende Basis um, z.B. {{formula}}f(x)=(\frac{1}{2})^x= 2^{-x}{{/formula}} ist eine Umwandlung in die neue Basis {{formula}}b=2{{/formula}}
27 27  {{formula}}f(x)=(\frac{1}{4})^x{{/formula}} in die neue Basis {{formula}}b=2{{/formula}}
... ... @@ -36,8 +36,6 @@
36 36  Bestimme zu jedem Schaubild eine passende Funktionsgleichung.
37 37  
38 38  [[image:Exponentialfunktionen.svg||width=600]]
39 -
40 -
41 41  {{/aufgabe}}
42 42  
43 43  {{aufgabe id="e-Funktion im Vergleich" afb="II" kompetenzen="K4" quelle="Niklas Wunder, Katharina Schneider" zeit="5"}}
... ... @@ -44,7 +44,6 @@
44 44  Gegeben ist der Graph zu {{formula}}f(x)=e^x{{/formula}}. Skizziere deine Vermutung wie die Graphen von {{formula}}g(x)=2^x{{/formula}} und {{formula}}h(x)=3^x{{/formula}} verlaufen.
45 45  (Ohne Taschenrechner, ohne Wertetabelle)
46 46  [[image:EFunktion.svg||width=500]]
47 -
48 48  {{/aufgabe}}
49 49  
50 50  {{aufgabe id="Eigenschaften der e-Funktion" afb="I" kompetenzen="K4" quelle="Niklas Wunder, Katharina Schneider" zeit="5"}}
... ... @@ -60,7 +60,6 @@
60 60  a) Welchem Muster lässt sich bei der Berechnung erkennen? Führe das Muster fort und berechne {{formula}} a_5, a_6
61 61  {{/formula}}.
62 62  b) Die eulersche Zahl {{formula}} e{{/formula}} ist gegben durch {{formula}} e= 2+\frac{1}{1\cdot 2}+\frac{1}{1\cdot 2\cdot 3}+\frac{1}{1\cdot 2\cdot 3\cdot 4}+ ...{{/formula}}, d.h durch Fortsetzung des Musters berechnet man die Zahl {{formula}} e{{/formula}} auf immer mehr Nachkommastellen. Gib die Zahl {{formula}} e{{/formula}} so genau an, wie du sie in a) berechnet hast. Hinweis: Du kannst gerne noch mehr weiter Zahlterme {{formula}} a_7,a_8, usw.{{/formula}}, wenn du eine noch höhere Genauigheit haben willst.
63 -
64 64  {{/aufgabe}}
65 65  
66 66  {{lehrende}}
graph f.svg
Author
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1 +XWiki.holgerengels
Größe
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1 +18.0 KB
Inhalt
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