Zum Inhalt springen
Zuletzt geändert von Stephanie Wietzorek am 2025/05/21 10:29
Von Version 47.2
bearbeitet von Holger Engels
am 2025/05/20 14:07
Änderungskommentar: Es gibt keinen Kommentar für diese Version
Auf Version 60.1
bearbeitet von Holger Engels
am 2025/05/20 16:03
Änderungskommentar: Neues Bild Aussagen.svg hochladen

Zusammenfassung

Details

Seiteneigenschaften
Inhalt
... ... @@ -1,6 +1,5 @@
1 1  {{seiteninhalt/}}
2 2  
3 -=== Kompetenzen ===
4 4  [[Kompetenzen.K4]] [[Kompetenzen.K5]] Ich kann Werte der Tangentensteigung graphisch bestimmen
5 5  [[Kompetenzen.K4]] [[Kompetenzen.K1]] Ich kann aus Werten der Tangentensteigung einen Graphen zeichnen und diesen als Graphen der Ableitungsfunktion deuten
6 6  [[Kompetenzen.K6]] Ich kann Zusammenhänge zwischen den beiden Funktionsgraphen beschreiben
... ... @@ -10,9 +10,6 @@
10 10  **Interaktiv Erkunden:** [[Graphisches Ableiten>>https://kmap.eu/app/browser/Mathematik/Differentialrechnung/Graphisches%20Ableiten#erkunden]]
11 11  {{/lernende}}
12 12  
13 -* Kann eine Tangente den Funktionsgraphen schneiden?
14 -
15 -* Bereiche mit positiver/ negativer Steigung schraffieren
16 16  * Punktweise graphisch ableiten
17 17  * Qualitativ graphisch ableiten
18 18  * Zusammenhänge HP, TP, SP vorwärts und rückwärts
... ... @@ -30,12 +30,12 @@
30 30  [[image:Tangenten einzeichnen 1.svg|| width="350px"]] [[image:Tangenten einzeichnen 2.svg|| width="350px"]] [[image:Tangenten einzeichnen 3.svg|| width="350px"]] [[image:Tangenten einzeichnen 4.svg|| width="350px"]]
31 31  {{/aufgabe}}
32 32  
33 -{{aufgabe id="Punkte mit gegebener Steigung finden" afb="?" kompetenzen="" quelle="Stephanie Wietzorek und Simone Kanzler" cc="BY-SA" zeit="3"}}
29 +{{aufgabe id="Punkte mit gegebener Steigung finden" afb="?" kompetenzen="" quelle="Stephanie Wietzorek und Simone Kanzler" cc="BY-SA" zeit="?"}}
34 34  Es ist das Schaubild {{formula}}K_f{{/formula}} einer Funktion {{formula}}f{{/formula}} gegeben. Kennzeichne Punkte auf {{formula}}K_f{{/formula}}, für die gilt:
35 - {{formula}}f'(x) =1{{/formula}}
36 - {{formula}}f'(x) =1,5{{/formula}}
37 - {{formula}}f'(x) =0{{/formula}}
38 - {{formula}}f'(x) = -\frac{17}{4}{{/formula}}
31 + die Steigung der Tangente in diesem Punkt ist 1
32 + die Steigung der Tangente in diesem Punkt ist 1,5
33 + die Steigung der Tangente in diesem Punkt ist 0
34 + die Steigung der Tangente in diesem Punkt ist {{formula}}-\frac{17}{4}{{/formula}}
39 39  [[image:Tangentensteigung.svg|| width="700px"]]
40 40  {{/aufgabe}}
41 41  
... ... @@ -47,17 +47,15 @@
47 47  | [[image:Polynome zuordnen i.svg||width=200]] | | | | | [[image:Polynome zuordnen D.svg||width=200]]
48 48  {{/aufgabe}}
49 49  
50 -{{aufgabe id="Skizzieren anhand Eigenschaften" afb="?" kompetenzen="" quelle=" Stephanie Wietzorek, Simone Kanzler" cc="BY-SA" zeit="4" interaktiv="Interaktiv Zuordnung"}}
51 -(% style="float:left; margin-right: 16px" %)
52 -Es ist ein zur y-Achse symmetrisches Schaubild einer Funktion 4. Grades gesucht. Folgende Angaben sind bekannt:
53 -
46 +{{aufgabe id="Skizzieren anhand Eigenschaften" afb="?" kompetenzen="" quelle="Stephanie Wietzorek, Simone Kanzler" cc="BY-SA" zeit="4"}}
47 +Es ist ein zur y-Achse symmetrisches Schaubild einer Funktion 4. Grades gesucht. Folgende Angaben sind bekannt, fülle die Lücken.
54 54  (% class="border" %)
55 -|= {{formula}}x{{/formula}} |-4|-1|0|1 |4
56 -|= {{formula}}f(x){{/formula}} |-2,5| |2 |0|
57 -|= {{formula}}f'(x){{/formula}} |-2| |0|-1 |
49 +|{{formula}}x{{/formula}}|-4|-1|0|1 |4
50 +|Funktionswert|-2,5| |2 |0|
51 +|Tangentensteigung|-2| |0|-1 |
58 58  {{/aufgabe}}
59 59  
60 -{{aufgabe id="Aussagen" afb="I" kompetenzen="" quelle="KMap" cc="BY-SA" zeit="3"}}
54 +{{aufgabe id="Aussagen Polynomfunktion I" afb="I" kompetenzen="" quelle="KMap" cc="BY-SA" zeit="3"}}
61 61  Prüfe die Aussagen! Welche sind wahr? Eine Polynomfunktion 3. Grades ..
62 62  ☐ hat immer zwei Extrempunkte!
63 63  ☐ kann auch mal nur einen Extrempunkt haben!
... ... @@ -66,4 +66,25 @@
66 66  ☐ hat entweder einen Sattelpunkt oder zwei Extrempunkte!
67 67  {{/aufgabe}}
68 68  
63 +{{aufgabe id="Aussagen Polynomfunktion II" afb="?" kompetenzen="" quelle="Stephanie Wietzorek, Simone Kanzler" cc="BY-SA" zeit="?"}}
64 +Eine weitere Funktion hat folgendes Schaubild. Nimm Stellung zu folgenden Aussagen und begründe deine Antwort.
65 +[[image:Aussagen.svg|| width="700px"]]
66 +☐ {{formula}}f(-3)=3{{/formula}}
67 +☐ {{formula}}x = 3{{/formula}} ist dreifache Nullstell
68 +☐ die Tangentensteigungen sind negativ für {{formula}}x \in ]2;5[{{/formula}}
69 +☐ die Steigung der Tangente an der Stelle {{formula}}x = 1<-2{{/formula}}
70 +☐ an der Stelle {{formula}}x = 2{{/formula}} liegt eine waagrechte Tangente
71 +☐ die Tangentensteigungen sind negativ für {{formula}}-4 < x < 2{{/formula}}
72 +☐ die Tangentensteigungen haben einen Vorzeichenwechsel bei {{formula}}x=-4{{/formula}} von ⊝ ⇾ ⊕
73 +{{/aufgabe}}
74 +
75 +{{aufgabe id="Aussagen Sattelstelle" afb="I" kompetenzen="" quelle="KMap" cc="BY-SA" zeit="3"}}
76 +Welche Aussagen treffen auf eine Sattelstelle zu?
77 +☐ Eine Sattelstelle hat eine waagrechte Asymptote
78 +☐ An einer Sattelstelle hat die Steigung ein Maximum oder ein Minimum
79 +☐ An einer Sattelstelle gibt es immer auch einen Krümmungswechsel
80 +☐ Eine Sattelstelle ist auch eine Wendestelle
81 +☐ Eine Sattelstelle kann auch eine Maximalstelle sein
82 +{{/aufgabe}}
83 +
69 69  {{seitenreflexion bildungsplan="" kompetenzen="" anforderungsbereiche="" kriterien="" menge=""/}}
Aussagen.ggb
Author
... ... @@ -1,0 +1,1 @@
1 +XWiki.wies
Größe
... ... @@ -1,0 +1,1 @@
1 +63.5 KB
Inhalt
Aussagen.svg
Author
... ... @@ -1,0 +1,1 @@
1 +XWiki.holgerengels
Größe
... ... @@ -1,0 +1,1 @@
1 +20.5 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="733" height="509"><defs><clipPath id="kMHLSZqUXTKK"><path fill="none" stroke="none" d=" M 0 0 L 733 0 L 733 509 L 0 509 L 0 0 Z"/></clipPath></defs><g transform="scale(1,1)" clip-path="url(#kMHLSZqUXTKK)"><g><rect fill="rgb(255,255,255)" stroke="none" x="0" y="0" width="733" height="509" fill-opacity="1"/><path fill="none" stroke="rgb(192,192,192)" paint-order="fill stroke markers" d=" M 30.5 0.5 L 30.5 509.5 M 30.5 0.5 L 30.5 509.5 M 92.5 0.5 L 92.5 509.5 M 154.5 0.5 L 154.5 509.5 M 216.5 0.5 L 216.5 509.5 M 278.5 0.5 L 278.5 509.5 M 403.5 0.5 L 403.5 509.5 M 465.5 0.5 L 465.5 509.5 M 527.5 0.5 L 527.5 509.5 M 589.5 0.5 L 589.5 509.5 M 651.5 0.5 L 651.5 509.5 M 713.5 0.5 L 713.5 509.5" 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 5.5 0.5 L 5.5 509.5 M 18.5 0.5 L 18.5 509.5 M 42.5 0.5 L 42.5 509.5 M 55.5 0.5 L 55.5 509.5 M 67.5 0.5 L 67.5 509.5 M 80.5 0.5 L 80.5 509.5 M 104.5 0.5 L 104.5 509.5 M 117.5 0.5 L 117.5 509.5 M 129.5 0.5 L 129.5 509.5 M 142.5 0.5 L 142.5 509.5 M 167.5 0.5 L 167.5 509.5 M 179.5 0.5 L 179.5 509.5 M 191.5 0.5 L 191.5 509.5 M 204.5 0.5 L 204.5 509.5 M 229.5 0.5 L 229.5 509.5 M 241.5 0.5 L 241.5 509.5 M 254.5 0.5 L 254.5 509.5 M 266.5 0.5 L 266.5 509.5 M 291.5 0.5 L 291.5 509.5 M 303.5 0.5 L 303.5 509.5 M 316.5 0.5 L 316.5 509.5 M 328.5 0.5 L 328.5 509.5 M 353.5 0.5 L 353.5 509.5 M 365.5 0.5 L 365.5 509.5 M 378.5 0.5 L 378.5 509.5 M 390.5 0.5 L 390.5 509.5 M 415.5 0.5 L 415.5 509.5 M 427.5 0.5 L 427.5 509.5 M 440.5 0.5 L 440.5 509.5 M 452.5 0.5 L 452.5 509.5 M 477.5 0.5 L 477.5 509.5 M 490.5 0.5 L 490.5 509.5 M 502.5 0.5 L 502.5 509.5 M 514.5 0.5 L 514.5 509.5 M 539.5 0.5 L 539.5 509.5 M 552.5 0.5 L 552.5 509.5 M 564.5 0.5 L 564.5 509.5 M 577.5 0.5 L 577.5 509.5 M 601.5 0.5 L 601.5 509.5 M 614.5 0.5 L 614.5 509.5 M 626.5 0.5 L 626.5 509.5 M 639.5 0.5 L 639.5 509.5 M 663.5 0.5 L 663.5 509.5 M 676.5 0.5 L 676.5 509.5 M 688.5 0.5 L 688.5 509.5 M 701.5 0.5 L 701.5 509.5 M 726.5 0.5 L 726.5 509.5" 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 0.5 L 733.5 0.5 M 0.5 0.5 L 733.5 0.5 M 0.5 62.5 L 733.5 62.5 M 0.5 124.5 L 733.5 124.5 M 0.5 187.5 L 733.5 187.5 M 0.5 249.5 L 733.5 249.5 M 0.5 311.5 L 733.5 311.5 M 0.5 435.5 L 733.5 435.5 M 0.5 497.5 L 733.5 497.5" 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 0.5 L 733.5 0.5 M 0.5 13.5 L 733.5 13.5 M 0.5 25.5 L 733.5 25.5 M 0.5 37.5 L 733.5 37.5 M 0.5 50.5 L 733.5 50.5 M 0.5 75.5 L 733.5 75.5 M 0.5 87.5 L 733.5 87.5 M 0.5 100.5 L 733.5 100.5 M 0.5 112.5 L 733.5 112.5 M 0.5 137.5 L 733.5 137.5 M 0.5 149.5 L 733.5 149.5 M 0.5 162.5 L 733.5 162.5 M 0.5 174.5 L 733.5 174.5 M 0.5 199.5 L 733.5 199.5 M 0.5 211.5 L 733.5 211.5 M 0.5 224.5 L 733.5 224.5 M 0.5 236.5 L 733.5 236.5 M 0.5 261.5 L 733.5 261.5 M 0.5 274.5 L 733.5 274.5 M 0.5 286.5 L 733.5 286.5 M 0.5 298.5 L 733.5 298.5 M 0.5 323.5 L 733.5 323.5 M 0.5 336.5 L 733.5 336.5 M 0.5 348.5 L 733.5 348.5 M 0.5 360.5 L 733.5 360.5 M 0.5 385.5 L 733.5 385.5 M 0.5 398.5 L 733.5 398.5 M 0.5 410.5 L 733.5 410.5 M 0.5 423.5 L 733.5 423.5 M 0.5 447.5 L 733.5 447.5 M 0.5 460.5 L 733.5 460.5 M 0.5 472.5 L 733.5 472.5 M 0.5 485.5 L 733.5 485.5" 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 340.5 2.5 L 340.5 509.5" stroke-opacity="1" stroke-miterlimit="10"/><path fill="none" stroke="rgb(37,37,37)" paint-order="fill stroke markers" d=" M 340.5 1.5 L 336.5 5.5" stroke-opacity="1" stroke-miterlimit="10"/><path fill="none" stroke="rgb(37,37,37)" paint-order="fill stroke markers" d=" M 340.5 1.5 L 344.5 5.5" stroke-opacity="1" stroke-miterlimit="10"/><text fill="rgb(37,37,37)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="16px" font-style="normal" font-weight="normal" text-decoration="normal" x="715" y="369" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">x</text><path fill="none" stroke="rgb(37,37,37)" paint-order="fill stroke markers" d=" M 0.5 373.5 L 731.5 373.5" stroke-opacity="1" stroke-miterlimit="10"/><path fill="none" stroke="rgb(37,37,37)" paint-order="fill stroke markers" d=" M 732.5 373.5 L 728.5 369.5" stroke-opacity="1" stroke-miterlimit="10"/><path fill="none" stroke="rgb(37,37,37)" paint-order="fill stroke markers" d=" M 732.5 373.5 L 728.5 377.5" 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="25" y="389" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="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="87" y="389" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">–4</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="149" y="389" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">–3</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="211" y="389" 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="273" y="389" 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="401" y="389" 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="463" y="389" 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="525" y="389" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">3</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="587" y="389" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">4</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="649" y="389" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="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="711" y="389" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">6</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="320" y="502" 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="320" y="440" 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="326" y="316" 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="326" y="254" 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="326" y="192" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">3</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="326" y="129" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">4</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="326" y="67" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="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="326" y="389" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">0</text><path fill="none" stroke="rgb(0,0,255)" paint-order="fill stroke markers" d=" M 42.23339843750006 -5.528407684867261 L 42.59130859375006 1.009157605798805 L 42.94921875000006 7.472402233124342 L 43.30712890625006 13.861804843516722 L 43.6650390625 20.177842173119927 L 44.02294921875 26.420989052333425 L 44.380859375 32.591718410315764 L 44.73876953125 38.69050127949322 L 45.0966796875 44.717806800059066 L 45.45458984375 50.67410222446779 L 45.8125 56.559852921926165 L 46.17041015625006 62.37552238287725 L 46.52832031250006 68.12157222348179 L 46.88623046875006 73.79846219009238 L 47.24414062500006 79.40665016372498 L 47.60205078125006 84.94659216452328 L 47.95996093750006 90.4187423562202 L 48.31787109375 95.82355305059224 L 48.67578125 101.16147471191385 L 49.03369140625 106.43295596139802 L 49.3916015625 111.63844358164039 L 49.74951171875 116.77838252105488 L 50.107421875 121.85321589830457 L 50.8232421875 131.80932931875958 L 51.5390625 141.51029236536505 L 52.25488281250006 150.95958456723204 L 52.97070312500006 160.16065660115393 L 53.68652343750006 169.11693043222215 L 54.40234375000006 177.8317994541282 L 55.1181640625 186.30862862915012 L 55.833984375 194.55075462782835 L 56.5498046875 202.56148596831994 L 57.265625 210.34410315544562 L 57.98144531250006 217.9018588194187 L 58.69726562500006 225.23797785426032 L 59.41308593750006 232.35565755590054 L 60.12890625 239.2580677599641 L 60.8447265625 245.9483509792447 L 61.560546875 252.4296225408596 L 62.2763671875 258.7049707230949 L 62.9921875 264.77745689193387 L 63.70800781250006 270.6501156372713 L 64.42382812500006 276.32595490881397 L 65.13964843750006 281.80795615166585 L 65.85546875000006 287.09907444159944 L 66.57128906250006 292.2022386200128 L 67.287109375 297.1203514285714 L 68.71875 306.41290420978254 L 70.15039062500006 314.99943782052077 L 71.58203125 322.9022482646546 L 73.013671875 330.14322676785594 L 74.4453125 336.7438640106984 L 75.87695312500006 342.72525434163646 L 77.30859375000006 348.10809996986103 L 80.171875 357.1590302748978 L 83.03515625 364.0545878749069 L 85.89843750000003 368.94669645305277 L 87.33007812500003 370.687322524878 L 88.76171875000006 371.9814010564816 L 89.47753906250006 372.4664232378651 L 90.193359375 372.84629036206803 L 90.90917968750003 373.12311735620443 L 91.62500000000003 373.29899743842685 L 92.34082031250003 373.3760022415643 L 93.05664062500003 373.35618193644626 L 93.77246093750003 373.24156535491187 L 94.48828125000003 373.0341601125049 L 95.919921875 372.34890875974116 L 96.63574218750003 371.87497289884874 L 97.35156250000003 371.31606911920136 L 100.21484375000003 368.26853550454825 L 103.07812500000003 364.0101255109908 L 105.94140625000003 358.65428348044566 L 108.80468750000003 352.30945346954877 L 111.66796875000003 345.07919957709424 L 114.53125000000003 337.06232498366353 L 117.39453125000003 328.35298970344485 L 120.25781250000003 319.0408270482436 L 123.12109375000003 309.21105880368265 L 124.552734375 304.1275261703403 L 125.98437500000003 298.9446091175933 L 127.41601562500003 293.6717701315488 L 128.84765625000003 288.3182171005973 L 130.279296875 282.8929067637541 L 131.71093750000003 277.40454813887817 L 133.14257812500003 271.8616059307695 L 134.57421875000003 266.27230391914395 L 136.005859375 260.64462832648604 L 137.43750000000003 254.98633116578011 L 138.86914062500003 249.3049335681194 L 140.30078125000003 243.6077290901928 L 141.732421875 237.90178700164975 L 143.16406250000003 232.1939555523429 L 144.59570312500003 226.4908652194495 L 146.02734375000003 220.79893193447003 L 147.458984375 215.12436029010433 L 148.89062500000003 209.47314672700733 L 150.32226562500003 203.85108270042144 L 151.75390625000003 198.26375782668714 L 153.185546875 192.71656300963187 L 154.61718750000003 187.21469354683626 L 156.04882812500003 181.76315221577963 L 157.48046875000003 176.36675233986216 L 158.912109375 171.0301208343049 L 160.34375000000003 165.75770123192956 L 161.77539062500003 160.5537566888142 L 163.20703125000003 155.42237296982807 L 164.638671875 150.36746141404421 L 166.07031250000003 145.3927618800293 L 168.93359375000003 135.69811843993472 L 171.79687500000003 126.36504256131443 L 174.66015625000003 117.41757558593642 L 177.52343750000003 108.87729099338588 L 180.38671875000003 100.76338382107429 L 183.25000000000003 93.09275879644065 L 186.11328125000003 85.88011718134265 L 188.97656250000003 79.13804232863748 L 191.83984375000003 72.8770839509528 L 194.70312500000003 67.10584110165024 L 197.56640625000003 61.831043867977996 L 200.42968750000003 57.057633776413695 L 206.15625000000003 49.026271739056654 L 211.88281250000003 43.01849025702745 L 214.74609375 40.76900525621397 L 217.609375 39.01733721540745 L 220.47265625 37.75805090930015 L 223.3359375 36.98451943341547 L 226.19921875 36.68899301916633 L 229.0625 36.86266656110229 L 231.92578125 37.49574585634832 L 234.7890625 38.5775125562339 L 237.65234375 40.09638783011138 L 240.515625 42.039994741366286 L 246.2421875 47.14827044110888 L 251.96875 53.789651199578316 L 257.6953125 61.842454578042634 L 263.421875 71.17777353275443 L 266.28515625000006 76.28453426217436 L 269.1484375 81.66116337297456 L 272.01171875 87.29025326602095 L 274.875 93.1542462991859 L 277.73828125000006 99.23548042183353 L 280.6015625 105.5162335214967 L 283.46484375 111.97876648274331 L 286.328125 118.60536495823376 L 289.19140625000006 125.37837985196845 L 292.0546875 132.28026651472587 L 294.91796875 139.29362265169152 L 297.78125 146.4012249422769 L 300.64453125000006 153.5860643721288 L 303.5078125 160.8313802773293 L 306.37109375 168.12069310078672 L 309.234375 175.43783586081648 L 312.09765625000006 182.7669843319119 L 314.9609375 190.09268593770656 L 317.82421875 197.39988735612684 L 320.6875 204.6739608367346 L 323.55078125000006 211.90072923026014 L 326.4140625 219.06648973032603 L 329.27734375 226.15803632736194 L 332.140625 233.16268097470885 L 335.00390625000006 240.06827346691398 L 337.8671875 246.86322003021664 L 340.73046875 253.53650062522487 L 343.59375 260.07768496178124 L 346.45703125000006 266.47694722602 L 349.3203125 272.7250795196149 L 352.18359375 278.81350401121693 L 355.046875 284.73428380008306 L 357.91015625000006 290.48013249189455 L 360.7734375 296.0444224867666 L 363.63671875 301.4211919794487 L 366.5 306.60515067171417 L 372.2265625 316.37685725688436 L 377.953125 325.3307859357779 L 383.6796875 333.44907375525963 L 389.40625 340.7247072575706 L 395.1328125 347.1613962025301 L 400.859375 352.7733648699271 L 406.5859375 357.58506094210236 L 412.3125 361.63078196672006 L 418.0390625 364.95421939972937 L 423.765625 367.607920228516 L 429.4921875 369.65266617524355 L 435.21875 371.1567704803851 L 440.9453125 372.1952922664443 L 446.671875 372.84916848186685 L 452.3984375 373.2042634251414 L 458.125 373.3503358490907 L 463.8515625 373.3799236453528 L 469.578125 373.3871461090517 L 475.3046875 373.4664237836583 L 481.03125 373.71111588604134 L 486.7578125 374.21207531170785 L 492.484375 375.0561212202338 L 498.2109375 376.32442920088494 L 503.9375 378.0908390184268 L 509.66406250000006 380.42007993912546 L 515.390625 383.3659136369377 L 521.1171875 386.9691946798914 L 526.84375 391.2558485966555 L 532.5703125 396.2347675233001 L 538.296875 401.8956234302466 L 544.0234375 408.20659892940756 L 549.75 415.11203566151687 L 555.4765625 422.53000026364896 L 561.203125 430.3497679169285 L 566.9296875 438.429223474431 L 572.65625 446.5921801692715 L 578.3828125 454.62561590288396 L 584.109375 462.276827113491 L 589.8359375 469.25050022476347 L 595.5625 475.20570067466934 L 601.2890625 479.7527795245127 L 604.15234375 481.36240786176757 L 607.015625 482.45019764816317 L 608.447265625 482.77859624485416 L 609.87890625 482.95231409769184 L 612.7421875 482.80126750147525 L 613.4580078125 482.65318358105685 L 614.173828125 482.458691994206 L 615.60546875 481.9258069007255 L 618.46875 480.2508124718964 L 619.900390625 479.0889304605332 L 621.33203125 477.6971866240255 L 624.1953125 474.1817438082665 L 627.05859375 469.61709903961207 L 629.921875 463.91155513080685 L 632.78515625 456.9689886384517 L 635.6484375 448.68873452129833 L 638.51171875 438.96546951073213 L 639.943359375 433.52849167262593 L 641.375 427.6890941934498 L 642.806640625 421.43274881684073 L 644.23828125 414.7446138063236 L 645.669921875 407.6095301497239 L 647.1015625 400.0120177434579 L 648.533203125 391.93627155670185 L 649.96484375 383.366157775436 L 651.396484375 374.2852099263725 L 652.828125 364.6766249807552 L 653.5439453125 359.66912465999786 L 654.259765625 354.523259438041 L 654.9755859375 349.23683253277744 L 655.69140625 343.8076253894577 L 656.4072265625 338.2333975565758 L 657.123046875 332.5118865614405 L 657.8388671875 326.64080778543234 L 658.5546875 320.61785433894715 L 659.2705078125 314.4406969360204 L 659.986328125 308.10698376864656 L 660.7021484375 301.61434038077465 L 661.41796875 294.9603695419943 L 662.1337890625 288.1426511209059 L 662.849609375 281.1587419581772 L 663.5654296875 274.0061757392847 L 664.28125 266.6824628669408 L 664.9970703125 259.18509033320714 L 665.712890625 251.51152159129276 L 666.4287109375 243.6591964270383 L 667.14453125 235.6255308300856 L 667.8603515625 227.40791686473312 L 668.576171875 219.00372254047656 L 669.2919921875 210.41029168223548 L 670.0078125 201.62494380026544 L 670.7236328125 192.64497395975692 L 671.439453125 183.46765265011263 L 672.1552734375 174.09022565392553 L 672.87109375 164.50991391562673 L 673.5869140625 154.72391340982776 L 674.302734375 144.72939500934555 L 674.66064453125 139.65305060003254 L 675.0185546875 134.5235043529139 L 675.37646484375 129.34039550825028 L 675.734375 124.10336171258032 L 676.09228515625 118.81203901455788 L 676.4501953125 113.46606186078805 L 676.80810546875 108.06506309165434 L 677.166015625 102.60867393714472 L 677.52392578125 97.09652401266897 L 677.8818359375 91.52824131487523 L 678.23974609375 85.90345221745741 L 678.59765625 80.22178146696143 L 678.95556640625 74.48285217858353 L 679.3134765625 68.68628583196647 L 679.67138671875 62.83170226698752 L 680.029296875 56.918719679545404 L 680.38720703125 50.94695461733852 L 680.7451171875 44.9160219756414 L 681.10302734375 38.82553499307346 L 681.4609375 32.675105247367924 L 681.81884765625 26.464342651123616 L 682.1767578125 20.192855447570707 L 682.53466796875 13.86025020631638 L 682.892578125 7.466131819089242 L 683.25048828125 1.0101034954828378 L 683.6083984375 -5.508233241311075" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="3.5"/><text fill="rgb(0,0,255)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="16px" font-style="normal" font-weight="normal" text-decoration="normal" x="52" y="31" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">K</text><text fill="rgb(0,0,255)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="14px" font-style="normal" font-weight="normal" text-decoration="normal" x="63" y="38" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">f</text></g></g></svg>