Änderungen von Dokument BPE 1.4 Lineare Funktionen

Zusammenfassung

• Seiteneigenschaften (4 geändert, 0 hinzugefügt, 0 gelöscht)
• Anhänge (0 geändert, 0 hinzugefügt, 4 gelöscht)
  • Graph0,5x 5.PNG
  • Steigung.svg
  • geraden.svg
  • sb geraden.png

Details

Seiteneigenschaften

Titel

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1		-BPE 1.4 Lineare Funktionen
	1	+BPE_1_4

Übergeordnete Seite

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1		-Eingangsklasse.WebHome
	1	+Main.WebHome

Dokument-Autor

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1		-XWiki.holgerengels
	1	+XWiki.holger

Inhalt

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1		-{{seiteninhalt/}}
	1	+{{box cssClass="floatinginfobox" title="**Contents**"}}{{toc /}}{{/box}}
2	2
3		-[[Kompetenzen.K4]] [[Kompetenzen.K5]] Ich kann Geraden als Graphen linearer Funktionen deuten
4		-[[Kompetenzen.K5]] Ich kann die Gleichungen besonderer Geraden angeben
5		-[[Kompetenzen.K1]] [[Kompetenzen.K5]] Ich kann begründen, dass eine Parallele zur y-Achse nicht Graph einer Funktion ist
6		-[[Kompetenzen.K5]] Ich kann den Steigungswinkel einer Geraden berechnen
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		-[[Kompetenzen.K5]] [[Kompetenzen.K1]] Ich kann lineare Ungleichungen geometrisch interpretieren
10		-[[Kompetenzen.K5]] Ich kann die Lösungsmengen linearer Ungleichungen mit Äquivalenzumformungen ermitteln
	3	+= Lineare Funktionen =
11	11
12		-{{lernende}}
13		-[[Interaktive Erkunden>>https://kmap.eu/app/browser/Mathematik/Lineare%20Funktionen/Hauptform#erkunden]]
14		-{{/lernende}}
15		-
16		-{{aufgabe id="Besondere Geraden" afb="I" kompetenzen="K4, K5" quelle="Holger Engels" cc="BY-SA" zeit="4"}}
17		-[[image:geraden.svg||style="float: right; width: 250px"]]Das Schaubild zeigt vier Geraden. Alle können als Gleichung ausgedrückt werden. Drei stellen auch einen funktionalen Zusammenhang dar.
18		-
19		-Gib jeweils eine Geradengleichungen und soweit möglich auch einen Funktionsterm an.
20		-
21		-Begründe, warum die vierte Gerade nicht Graph einer Funktion sein kann.
22		-{{/aufgabe}}
23		-
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.
26		-
27		-Für eine Taxifahrt fallen zunächst 5 Euro für die Anfahrt an. Dazu kommen pro angefangener gefahrener Minute 0,75 Euro.
28		-Es werden Fahrten von 5 Minuten, 10 Minuten und 15 Minuten durchgeführt.
29		-{{/aufgabe}}
30		-
31		-{{aufgabe id="Funktionsvorschriften zuordnen" afb="I" kompetenzen="K4, K5" quelle="Sabine Schäfer" cc="BY-SA" zeit="5"}}
32		-[[image:sb geraden.png||style="float: right" width="400"]]Das Schaubild zeigt die Graphen von linearen Funktionen. Ordne die folgenden Funktionsvorschriften begründet zu.
33		-
34		-a) {{formula}}f\left(x\right)=x-1;x\in\mathbb{R} {{/formula}}
35		-b) {{formula}}f\left(x\right)=1 - x^2;x\in\mathbb{R}{{/formula}}
36		-c) {{formula}}f\left(x\right)=\frac23x-2;x\in\mathbb{R}{{/formula}}
37		-d) {{formula}}f\left(x\right)=-\frac14x-1;x\in\mathbb{R}{{/formula}}
38		-e) {{formula}}f\left(x\right)=-0,25 x-2;x\in\mathbb{R}{{/formula}}
39		-f) {{formula}}f\left(x\right)=2 - 2x;x\in\mathbb{R}{{/formula}}
40		-{{/aufgabe}}
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		-{{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		-[[image:Graph0,5x+5.PNG||width="220" style="float: right"]]
48		-Die Abbildung zeigt den Graphen der in {{formula}}\mathbb{R}{{/formula}} definierten linearen Funktion {{formula}} f{{/formula}}.
49		-(% style="list-style: alphastyle" %)
50		-1. Begründe, dass {{formula}}f(x)=\frac{1}{2}x+5{{/formula}} gilt.
51		-1. Berechne den Abstand des Koordinatenursprungs zum Graphen.
52		-{{/aufgabe}}
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		-{{aufgabe id="Geradengleichung transformieren" afb="II" kompetenzen="" quelle="Kim Fujan" cc="BY-SA" zeit="5"}}
66		-Gegeben sei die Funktion {{formula}}f\left(x\right)=\frac{5}{4}x-4{{/formula}}.\\
67		-
68		-Gebe jeweils die neue Funktionsgleichung an, wenn der Graph von {{formula}}K_{f}{{/formula}}
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}}
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}}
83		-
84		-{{aufgabe id="Tarife" afb="I" kompetenzen="" quelle="Holger Engels" cc="BY-SA" zeit="5"}}
85		-Vergleiche die beiden Stromtarife:
86		-f(x) = 20 + 0,3
87		-g(x) = 40 + 0,2
88		-Für welchen Verbrauch ist f günstiger als g?
89		-{{/aufgabe}}
90		-
91		-{{seitenreflexion bildungsplan="3" kompetenzen="3" anforderungsbereiche="1" kriterien="2" menge="1"/}}
92		-
93		-
	5	+Die Schülerinnen und Schüler deuten Geraden als Graphen linearer Funktionen. Sie geben die Gleichungen besonderer Geraden an und begründen, dass eine Parallele zur y-Achse nicht Graph einer Funktion ist. Sie berechnen den Steigungswinkel einer Geraden und deuten ihn grafisch. Sie interpretieren lineare Ungleichungen geometrisch und ermitteln die Lösungsmengen mit Äquivalenzumformungen. Ebenso untersuchen die Schülerinnen und Schüler die Lagebeziehung zweier Geraden anhand ihrer Gleichungen und der Orthogonalitätsbedingung.

Graph0,5x 5.PNG

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1		-XWiki.akukin

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1		-71.7 KB

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Steigung.svg

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1		-XWiki.holgerengels

Größe

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