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Änderungen von Dokument BPE 1.4 Lineare Funktionen

Zuletzt geändert von Holger Engels am 2024/11/20 21:57
Von Version 47.1
bearbeitet von Holger Engels
am 2024/10/14 17:56
Änderungskommentar: Es gibt keinen Kommentar für diese Version
Auf Version 41.1
bearbeitet von Kim Fujan
am 2024/10/14 15:00
Änderungskommentar: Es gibt keinen Kommentar für diese Version

Zusammenfassung

Details

Seiteneigenschaften
Dokument-Autor
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1 -XWiki.holgerengels
1 +XWiki.fujan
Inhalt
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5 5  [[Kompetenzen.K1]] [[Kompetenzen.K5]] Ich kann begründen, dass eine Parallele zur y-Achse nicht Graph einer Funktion ist
6 6  [[Kompetenzen.K5]] Ich kann den Steigungswinkel einer Geraden berechnen
7 7  [[Kompetenzen.K4]] Ich kann den Steigungswinkel einer Geraden graphisch deuten
8 -[[Kompetenzen.K5]] Ich kann die Lagebeziehung zweier Geraden anhand ihrer Gleichungen und der Orthogonalitätsbedingung untersuchen
9 9  [[Kompetenzen.K5]] [[Kompetenzen.K1]] Ich kann lineare Ungleichungen geometrisch interpretieren
10 10  [[Kompetenzen.K5]] Ich kann die Lösungsmengen linearer Ungleichungen mit Äquivalenzumformungen ermitteln
10 +[[Kompetenzen.K5]] Ich kann die Lagebeziehung zweier Geraden anhand ihrer Gleichungen und der Orthogonalitätsbedingung untersuchen
11 11  
12 12  {{lernende}}
13 13  [[Interaktive Erkunden>>https://kmap.eu/app/browser/Mathematik/Lineare%20Funktionen/Hauptform#erkunden]]
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22 22  {{/aufgabe}}
23 23  
24 24  {{aufgabe id="Taxifahrt" afb="I" kompetenzen="K1, K4, K5" quelle="Sabine Schäfer" cc="BY-SA" zeit="5"}}
25 -Stelle folgende Situation grafisch dar und bestimme eine Gleichung, die den Sachverhalt ebenfalls beschreibt.
25 +Stellen Sie folgende Situation grafisch dar und bestimmen Sie eine Gleichung, die den Sachverhalt ebenfalls beschreibt.
26 26  
27 27  Für eine Taxifahrt fallen zunächst 5 Euro für die Anfahrt an. Dazu kommen pro angefangener gefahrener Minute 0,75 Euro.
28 28  Es werden Fahrten von 5 Minuten, 10 Minuten und 15 Minuten durchgeführt.
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39 39  f) {{formula}}f\left(x\right)=2 - 2x;x\in\mathbb{R}{{/formula}}
40 40  {{/aufgabe}}
41 41  
42 -{{aufgabe id="Steigung" afb="I" kompetenzen="" zeit="8" quelle="Holger Engels" cc="BY-SA"}}
43 -Die Baldwin Street im North East Valley ist mit einer maximalen Steigung von 1:2,86 die steilste Straße der Welt. Gib ihre Steigung in Prozent an und berechne den Steigungswinkel.
44 -{{/aufgabe}}
45 -
46 46  {{aufgabe id="Abstand Graph Koordinatenursprung" afb="II" kompetenzen="K1,K2,K4,K5" zeit="8" quelle="[[IQB e.V.>>https://www.iqb.hu-berlin.de/abitur/pools2023/abitur/pools2023/mathematik/grundlegend/2023_M_grundlege_7.pdf]]" niveau="g" tags="iqb" cc="BY"}}
47 47  [[image:Graph0,5x+5.PNG||width="220" style="float: right"]]
48 48  Die Abbildung zeigt den Graphen der in {{formula}}\mathbb{R}{{/formula}} definierten linearen Funktion {{formula}} f{{/formula}}.
49 -(% style="list-style: alphastyle" %)
50 50  1. Begründe, dass {{formula}}f(x)=\frac{1}{2}x+5{{/formula}} gilt.
51 51  1. Berechne den Abstand des Koordinatenursprungs zum Graphen.
52 52  {{/aufgabe}}
53 53  
54 -{{aufgabe id="" afb="I" kompetenzen="" quelle="Holger Engels" cc="BY-SA" zeit="5"}}
55 -Bestimme jeweils den Steigungswinkel und die Steigung in Prozent.
56 -(% style="list-style: alphastyle" %)
57 -1. {{formula}}g(x)=\frac{1}{2}x+1{{/formula}}
58 -1. [[image:Steigung.svg||width=300]]
59 -{{/aufgabe}}
60 -
61 -{{aufgabe id="" afb="I" kompetenzen="" quelle="Holger Engels" cc="BY-SA" zeit="5"}}
62 -Bestimme den Funktionsterm einer linearen Funktion //h//, deren Graph orthogonal zu dem der Funktion //g// mit {{formula}}g(x)=3x-2{{/formula}} ist und durch den Punkt //P(-2|1)// verläuft.
63 -{{/aufgabe}}
64 -
65 65  {{aufgabe id="Geradengleichung transformieren" afb="II" kompetenzen="" quelle="Kim Fujan" cc="BY-SA" zeit="5"}}
66 66  Gegeben sei die Funktion {{formula}}f\left(x\right)=\frac{5}{4}x-4{{/formula}}.\\
67 67  
68 -Gebe jeweils die neue Funktionsgleichung an, wenn der Graph von {{formula}}K_{f}{{/formula}}
52 +Geben Sie jeweils die neue Funktionsgleichung an, wenn der Graph von {{formula}}K_{f}{{/formula}}
69 69  
70 -(% style="list-style: alphastyle" %)
71 -1. zuerst um 3 nach oben verschoben,
72 -1. anschließend an der x-Achse gespiegelt
73 -1. und abschließend an der y-Achse gespiegelt wird.
74 -{{/aufgabe}}
54 +a) zuerst um 3 nach oben verschoben,
55 +b) anschließend an der x-Achse gespiegelt
56 +c) und abschließend an der y-Achse gespiegelt wird.
57 + {{/aufgabe}}
75 75  
76 -{{aufgabe id="Ungleichung" afb="I" kompetenzen="" quelle="Holger Engels" cc="BY-SA" zeit="5"}}
77 -Kim rechnet folgendes ..
78 -{{formula}}-2x+1 > 0 | -1{{/formula}}
79 -{{formula}}\Leftrightarrow -2x > -1 | :(-2){{/formula}}
80 -{{formula}}\Leftrightarrow x > 2{{/formula}}
81 -.. und stellt bei der Probe fest, dass irgendwas schief gelaufen sein muss. Erkläre!
82 -{{/aufgabe}}
59 +{{seitenreflexion kompetenzen="3" anforderungsbereiche="1" kriterien="2" menge="1"/}}
83 83  
84 -{{aufgabe id="Tarife" afb="I" kompetenzen="" quelle="Holger Engels" cc="BY-SA" zeit="5"}}
85 -Vergleiche die beiden Stromtarife:
86 -{{formula}}f(x) = 20 + 0,3x{{/formula}}
87 -{{formula}}g(x) = 40 + 0,2x{{/formula}}
88 -Für welchen Verbrauch ist der Tarif mit dem höheren Grundbetrag günstiger?
89 -{{/aufgabe}}
90 90  
91 -{{seitenreflexion bildungsplan="3" kompetenzen="3" anforderungsbereiche="1" kriterien="2" menge="1"/}}
92 -
93 -
Steigung.svg
Author
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1 -XWiki.holgerengels
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Inhalt
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