Änderungen von Dokument BPE 3.2 Funktionsgraph
Zuletzt geändert von Holger Engels am 2025/03/31 21:43
Von Version 45.3
bearbeitet von Holger Engels
am 2024/11/15 10:11
am 2024/11/15 10:11
Änderungskommentar:
Kommentar bearbeiten
Auf Version 54.1
bearbeitet von Holger Engels
am 2024/11/15 15:19
am 2024/11/15 15:19
Änderungskommentar:
Es gibt keinen Kommentar für diese Version
Zusammenfassung
-
Seiteneigenschaften (1 geändert, 0 hinzugefügt, 0 gelöscht)
-
Anhänge (0 geändert, 2 hinzugefügt, 0 gelöscht)
-
Objekte (1 geändert, 2 hinzugefügt, 0 gelöscht)
Details
- Seiteneigenschaften
-
- Inhalt
-
... ... @@ -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 +23,42 @@ 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}} 60 + 61 +{{aufgabe id="Fertig zeichnen" afb="I" kompetenzen="" quelle="Stefanie Schmidt" cc="by-sa" zeit="3"}} 62 +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}}. 63 +[[image:Fertig zeichnen.svg]] 64 +{{/aufgabe}}
- Fertig zeichnen.ggb
-
- Author
-
... ... @@ -1,0 +1,1 @@ 1 +XWiki.holgerengels - Größe
-
... ... @@ -1,0 +1,1 @@ 1 +41.0 KB - Inhalt
- Fertig zeichnen.svg
-
- Author
-
... ... @@ -1,0 +1,1 @@ 1 +XWiki.holgerengels - Größe
-
... ... @@ -1,0 +1,1 @@ 1 +22.7 KB - Inhalt
-
... ... @@ -1,0 +1,1 @@ 1 +<svg version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="624" height="384"><defs><clipPath id="DxhOEzrTSMaV"><path fill="none" stroke="none" d=" M 0 0 L 624 0 L 624 384 L 0 384 L 0 0 Z"/></clipPath></defs><g transform="scale(1,1)" clip-path="url(#DxhOEzrTSMaV)"><g><rect fill="rgb(255,255,255)" stroke="none" x="0" y="0" width="625" height="385" fill-opacity="1"/><path fill="none" stroke="rgb(192,192,192)" paint-order="fill stroke markers" d=" M 22.5 0.5 L 22.5 384.5 M 22.5 0.5 L 22.5 384.5 M 78.5 0.5 L 78.5 384.5 M 135.5 0.5 L 135.5 384.5 M 191.5 0.5 L 191.5 384.5 M 248.5 0.5 L 248.5 384.5 M 361.5 0.5 L 361.5 384.5 M 418.5 0.5 L 418.5 384.5 M 475.5 0.5 L 475.5 384.5 M 531.5 0.5 L 531.5 384.5 M 588.5 0.5 L 588.5 384.5" stroke-opacity="1" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10"/><path fill="none" stroke="rgb(192,192,192)" paint-order="fill stroke markers" d=" M 10.5 0.5 L 10.5 384.5 M 33.5 0.5 L 33.5 384.5 M 44.5 0.5 L 44.5 384.5 M 55.5 0.5 L 55.5 384.5 M 67.5 0.5 L 67.5 384.5 M 89.5 0.5 L 89.5 384.5 M 101.5 0.5 L 101.5 384.5 M 112.5 0.5 L 112.5 384.5 M 123.5 0.5 L 123.5 384.5 M 146.5 0.5 L 146.5 384.5 M 157.5 0.5 L 157.5 384.5 M 169.5 0.5 L 169.5 384.5 M 180.5 0.5 L 180.5 384.5 M 203.5 0.5 L 203.5 384.5 M 214.5 0.5 L 214.5 384.5 M 225.5 0.5 L 225.5 384.5 M 237.5 0.5 L 237.5 384.5 M 259.5 0.5 L 259.5 384.5 M 271.5 0.5 L 271.5 384.5 M 282.5 0.5 L 282.5 384.5 M 293.5 0.5 L 293.5 384.5 M 316.5 0.5 L 316.5 384.5 M 327.5 0.5 L 327.5 384.5 M 339.5 0.5 L 339.5 384.5 M 350.5 0.5 L 350.5 384.5 M 373.5 0.5 L 373.5 384.5 M 384.5 0.5 L 384.5 384.5 M 395.5 0.5 L 395.5 384.5 M 407.5 0.5 L 407.5 384.5 M 429.5 0.5 L 429.5 384.5 M 441.5 0.5 L 441.5 384.5 M 452.5 0.5 L 452.5 384.5 M 463.5 0.5 L 463.5 384.5 M 486.5 0.5 L 486.5 384.5 M 497.5 0.5 L 497.5 384.5 M 508.5 0.5 L 508.5 384.5 M 520.5 0.5 L 520.5 384.5 M 542.5 0.5 L 542.5 384.5 M 554.5 0.5 L 554.5 384.5 M 565.5 0.5 L 565.5 384.5 M 576.5 0.5 L 576.5 384.5 M 599.5 0.5 L 599.5 384.5 M 610.5 0.5 L 610.5 384.5 M 622.5 0.5 L 622.5 384.5" stroke-opacity="0.23529411764705882" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10"/><path fill="none" stroke="rgb(192,192,192)" paint-order="fill stroke markers" d=" M 0.5 21.5 L 624.5 21.5 M 0.5 21.5 L 624.5 21.5 M 0.5 77.5 L 624.5 77.5 M 0.5 134.5 L 624.5 134.5 M 0.5 247.5 L 624.5 247.5 M 0.5 304.5 L 624.5 304.5 M 0.5 360.5 L 624.5 360.5" stroke-opacity="1" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10"/><path fill="none" stroke="rgb(192,192,192)" paint-order="fill stroke markers" d=" M 0.5 9.5 L 624.5 9.5 M 0.5 9.5 L 624.5 9.5 M 0.5 32.5 L 624.5 32.5 M 0.5 43.5 L 624.5 43.5 M 0.5 55.5 L 624.5 55.5 M 0.5 66.5 L 624.5 66.5 M 0.5 89.5 L 624.5 89.5 M 0.5 100.5 L 624.5 100.5 M 0.5 111.5 L 624.5 111.5 M 0.5 123.5 L 624.5 123.5 M 0.5 145.5 L 624.5 145.5 M 0.5 157.5 L 624.5 157.5 M 0.5 168.5 L 624.5 168.5 M 0.5 179.5 L 624.5 179.5 M 0.5 202.5 L 624.5 202.5 M 0.5 213.5 L 624.5 213.5 M 0.5 225.5 L 624.5 225.5 M 0.5 236.5 L 624.5 236.5 M 0.5 259.5 L 624.5 259.5 M 0.5 270.5 L 624.5 270.5 M 0.5 281.5 L 624.5 281.5 M 0.5 293.5 L 624.5 293.5 M 0.5 315.5 L 624.5 315.5 M 0.5 326.5 L 624.5 326.5 M 0.5 338.5 L 624.5 338.5 M 0.5 349.5 L 624.5 349.5 M 0.5 372.5 L 624.5 372.5 M 0.5 383.5 L 624.5 383.5" stroke-opacity="0.23529411764705882" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10"/><path fill="none" stroke="rgb(37,37,37)" paint-order="fill stroke markers" d=" M 305.5 2.5 L 305.5 384.5" stroke-opacity="1" stroke-miterlimit="10"/><path fill="none" stroke="rgb(37,37,37)" paint-order="fill stroke markers" d=" M 305.5 1.5 L 301.5 5.5" stroke-opacity="1" stroke-miterlimit="10"/><path fill="none" stroke="rgb(37,37,37)" paint-order="fill stroke markers" d=" M 305.5 1.5 L 309.5 5.5" stroke-opacity="1" stroke-miterlimit="10"/><path fill="none" stroke="rgb(37,37,37)" paint-order="fill stroke markers" d=" M 0.5 191.5 L 622.5 191.5" stroke-opacity="1" stroke-miterlimit="10"/><path fill="none" stroke="rgb(37,37,37)" paint-order="fill stroke markers" d=" M 623.5 191.5 L 619.5 187.5" stroke-opacity="1" stroke-miterlimit="10"/><path fill="none" stroke="rgb(37,37,37)" paint-order="fill stroke markers" d=" M 623.5 191.5 L 619.5 195.5" stroke-opacity="1" stroke-miterlimit="10"/><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="11" y="207" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">–2.5</text><text fill="none" stroke="rgb(255,255,255)" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="11" y="207" text-anchor="start" dominant-baseline="alphabetic" stroke-opacity="1" stroke-linejoin="bevel" stroke-miterlimit="10" stroke-width="3">–2.5</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="11" y="207" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">–2.5</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="73" y="207" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">–2</text><text fill="none" stroke="rgb(255,255,255)" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="73" y="207" text-anchor="start" dominant-baseline="alphabetic" stroke-opacity="1" stroke-linejoin="bevel" stroke-miterlimit="10" stroke-width="3">–2</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="73" y="207" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">–2</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="124" y="207" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">–1.5</text><text fill="none" stroke="rgb(255,255,255)" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="124" y="207" text-anchor="start" dominant-baseline="alphabetic" stroke-opacity="1" stroke-linejoin="bevel" stroke-miterlimit="10" stroke-width="3">–1.5</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="124" y="207" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">–1.5</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="186" y="207" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">–1</text><text fill="none" stroke="rgb(255,255,255)" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="186" y="207" text-anchor="start" dominant-baseline="alphabetic" stroke-opacity="1" stroke-linejoin="bevel" stroke-miterlimit="10" stroke-width="3">–1</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="186" y="207" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">–1</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="237" y="207" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">–0.5</text><text fill="none" stroke="rgb(255,255,255)" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="237" y="207" text-anchor="start" dominant-baseline="alphabetic" stroke-opacity="1" stroke-linejoin="bevel" stroke-miterlimit="10" stroke-width="3">–0.5</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="237" y="207" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">–0.5</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="353" y="207" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">0.5</text><text fill="none" stroke="rgb(255,255,255)" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="353" y="207" text-anchor="start" dominant-baseline="alphabetic" stroke-opacity="1" stroke-linejoin="bevel" stroke-miterlimit="10" stroke-width="3">0.5</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="353" y="207" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">0.5</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="416" y="207" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">1</text><text fill="none" stroke="rgb(255,255,255)" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="416" y="207" text-anchor="start" dominant-baseline="alphabetic" stroke-opacity="1" stroke-linejoin="bevel" stroke-miterlimit="10" stroke-width="3">1</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="416" y="207" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">1</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="467" y="207" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">1.5</text><text fill="none" stroke="rgb(255,255,255)" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="467" y="207" text-anchor="start" dominant-baseline="alphabetic" stroke-opacity="1" stroke-linejoin="bevel" stroke-miterlimit="10" stroke-width="3">1.5</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="467" y="207" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">1.5</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="529" y="207" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">2</text><text fill="none" stroke="rgb(255,255,255)" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="529" y="207" text-anchor="start" dominant-baseline="alphabetic" stroke-opacity="1" stroke-linejoin="bevel" stroke-miterlimit="10" stroke-width="3">2</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="529" y="207" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">2</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="580" y="207" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">2.5</text><text fill="none" stroke="rgb(255,255,255)" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="580" y="207" text-anchor="start" dominant-baseline="alphabetic" stroke-opacity="1" stroke-linejoin="bevel" stroke-miterlimit="10" stroke-width="3">2.5</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="580" y="207" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">2.5</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="275" y="365" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">–1.5</text><text fill="none" stroke="rgb(255,255,255)" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="275" y="365" text-anchor="start" dominant-baseline="alphabetic" stroke-opacity="1" stroke-linejoin="bevel" stroke-miterlimit="10" stroke-width="3">–1.5</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="275" y="365" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">–1.5</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="285" y="309" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">–1</text><text fill="none" stroke="rgb(255,255,255)" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="285" y="309" text-anchor="start" dominant-baseline="alphabetic" stroke-opacity="1" stroke-linejoin="bevel" stroke-miterlimit="10" stroke-width="3">–1</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="285" y="309" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">–1</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="275" y="252" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">–0.5</text><text fill="none" stroke="rgb(255,255,255)" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="275" y="252" text-anchor="start" dominant-baseline="alphabetic" stroke-opacity="1" stroke-linejoin="bevel" stroke-miterlimit="10" stroke-width="3">–0.5</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="275" y="252" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">–0.5</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="281" y="139" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">0.5</text><text fill="none" stroke="rgb(255,255,255)" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="281" y="139" text-anchor="start" dominant-baseline="alphabetic" stroke-opacity="1" stroke-linejoin="bevel" stroke-miterlimit="10" stroke-width="3">0.5</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="281" y="139" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">0.5</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="291" y="82" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">1</text><text fill="none" stroke="rgb(255,255,255)" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="291" y="82" text-anchor="start" dominant-baseline="alphabetic" stroke-opacity="1" stroke-linejoin="bevel" stroke-miterlimit="10" stroke-width="3">1</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="291" y="82" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">1</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="281" y="26" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">1.5</text><text fill="none" stroke="rgb(255,255,255)" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="281" y="26" text-anchor="start" dominant-baseline="alphabetic" stroke-opacity="1" stroke-linejoin="bevel" stroke-miterlimit="10" stroke-width="3">1.5</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="281" y="26" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">1.5</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="291" y="207" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">0</text><text fill="none" stroke="rgb(255,255,255)" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="291" y="207" text-anchor="start" dominant-baseline="alphabetic" stroke-opacity="1" stroke-linejoin="bevel" stroke-miterlimit="10" stroke-width="3">0</text><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="12px" font-style="normal" font-weight="normal" text-decoration="normal" x="291" y="207" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">0</text><path fill="none" stroke="rgb(46,125,50)" paint-order="fill stroke markers" d=" M 44.484375 390.3482137258197 L 45.09375 381.4788504312663 L 45.703125 372.88065471223507 L 46.31250000000006 364.548509957017 L 46.921875 356.4773638624649 L 47.53125 348.6622278980957 L 48.140625 341.0981767729153 L 48.75 333.7803479049477 L 49.35937500000003 326.70394089346735 L 49.96875000000003 319.8642169939295 L 50.578125 313.2564985955847 L 51.1875 306.8761687017812 L 51.796875 300.7186704129424 L 52.40625000000003 294.7795064122138 L 53.01562500000003 289.0542384537759 L 53.62500000000003 283.5384868538107 L 54.234375 278.227929984123 L 54.84375 273.1183037684054 L 56.06250000000003 263.485071749133 L 57.28125 254.60581024733023 L 58.50000000000003 246.44842774746274 L 59.71875000000003 238.9817061092718 L 60.9375 232.17528507630973 L 62.15625000000003 225.999646950056 L 63.375 220.42610142879155 L 65.81250000000003 210.974574158359 L 68.25000000000003 203.60716296570203 L 73.125 194.33154808158707 L 73.73437500000006 193.62727824523733 L 74.34374999999997 193.01499772956817 L 75.56250000000003 192.05592450590785 L 76.171875 191.70399618758398 L 76.78125 191.43378514129114 L 78.00000000000003 191.12869438303537 L 78.60937500000003 191.08900479082237 L 79.21875 191.12141190137083 L 80.4375 191.3933293490253 L 81.04687500000003 191.62834259539525 L 81.65625000000003 191.9264575732945 L 82.875 192.70341397978018 L 85.3125 194.92223899089652 L 87.75000000000003 197.92240409188278 L 92.62500000000003 205.80138223915014 L 97.50000000000003 215.49283260778412 L 99.93750000000003 220.78790284106896 L 102.37500000000003 226.27435018925993 L 104.8125 231.87960621192084 L 107.25 237.53756928643153 L 109.68750000000003 243.18828963884698 L 112.125 248.7776629818618 L 114.56250000000003 254.25713265515319 L 117 259.58340016337513 L 119.43750000000003 264.71814400707876 L 121.875 269.6277467018305 L 126.75 278.6589973761121 L 131.62500000000003 286.4924251403359 L 136.50000000000003 293.00243432826966 L 141.37500000000003 298.1152043899639 L 146.25000000000003 301.80181075559216 L 148.6875 303.1119517816686 L 151.12500000000003 304.07180942149756 L 153.5625 304.6876121536731 L 156 304.9672718534438 M 156 304.9672718534438 L 160.875 304.5572568020683 L 162.09375000000003 304.26101727727695 L 163.31250000000003 303.89039071701825 L 165.75 302.93270562553533 L 170.625 300.2017477143868 L 175.5 296.4854026135877 L 180.375 291.91366543676565 L 185.25000000000003 286.62196216764056 L 190.125 280.74796144364285 L 195 274.4287294167184 L 199.875 267.79821428631703 L 204.75 260.9850470995631 L 209.625 254.11064541360528 L 214.5 247.28760641514396 L 219.375 240.61837609213325 L 224.25 234.19418105265578 L 229.125 228.09420958596834 L 234 222.38502856071506 M 234 222.38502856071506 L 238.875 217.12022275530694 L 243.75 212.34024321546505 L 248.625 208.07245123392485 L 253.5 204.33134454729998 L 258.375 201.1189523451027 L 263.25 198.425385685919 L 268.125 196.22952991573604 L 273 194.49986568341984 M 273 194.49986568341984 L 277.875 193.19540514834057 L 282.75 192.26672997514353 L 287.625 191.6571177106634 L 292.5 191.3037431379796 M 292.5 191.3037431379796 L 297.375 191.13894120261028 L 302.25 191.09151810584294 M 302.25 191.09151810584294 L 305.1419538285954 191.0889313372992" stroke-opacity="0.8" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><text fill="rgb(46,125,50)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="16px" font-style="normal" font-weight="normal" text-decoration="normal" x="45" y="376" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">f</text><text fill="none" stroke="rgb(255,255,255)" font-family="geogebra-sans-serif, sans-serif" font-size="16px" font-style="normal" font-weight="normal" text-decoration="normal" x="45" y="376" text-anchor="start" dominant-baseline="alphabetic" stroke-opacity="1" stroke-linejoin="bevel" stroke-miterlimit="10" stroke-width="3">f</text><text fill="rgb(46,125,50)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="16px" font-style="normal" font-weight="normal" text-decoration="normal" x="45" y="376" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">f</text></g></g></svg>
- XWiki.XWikiComments[0]
-
- Kommentar
-
... ... @@ -1,1 +1,1 @@ 1 -Aufgabe "Schnittpunkte mit den Koordinatenachsen bestimmen" überarbeiten. Aufgabe "Zuordnung Vielfachheiten" dazu.1 +Lösung zu Aufgabe "Schnittpunkte mit den Koordinatenachsen bestimmen" überarbeiten.
- XWiki.XWikiComments[1]
-
- Autor
-
... ... @@ -1,0 +1,1 @@ 1 +XWiki.holgerengels - Kommentar
-
... ... @@ -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
-
... ... @@ -1,0 +1,1 @@ 1 +2024-11-15 10:37:19.20
- XWiki.XWikiComments[2]
-
- Autor
-
... ... @@ -1,0 +1,1 @@ 1 +XWiki.holgerengels - Kommentar
-
... ... @@ -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
-
... ... @@ -1,0 +1,1 @@ 1 +2024-11-15 11:17:25.685