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Zuletzt geändert von Stephanie Wietzorek am 2025/05/21 10:29
Von Version 41.1
bearbeitet von Holger Engels
am 2025/05/20 13:53
Änderungskommentar: Neues Bild Polynome zuordnen f.svg hochladen
Auf Version 49.1
bearbeitet von Stephanie Wietzorek
am 2025/05/20 14:23
Änderungskommentar: Neues Bild Aussagen.svg hochladen

Zusammenfassung

Details

Seiteneigenschaften
Dokument-Autor
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1 -XWiki.holgerengels
1 +XWiki.wies
Inhalt
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18 18  * Zusammenhänge HP, TP, SP vorwärts und rückwärts
19 19  
20 20  * Funktionsterm der Ableitungsfunktion aus Tangentensteigungen aufstellen
21 -* Zuordnung Polynomfunktionen
22 22  * Beobachtungen bei e^x
23 23  
24 24  {{aufgabe id="Tangenten einzeichnen" afb="I" kompetenzen="" quelle="Holger Engels" cc="BY-SA" zeit="3"}}
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48 48  | [[image:Polynome zuordnen i.svg||width=200]] | | | | | [[image:Polynome zuordnen D.svg||width=200]]
49 49  {{/aufgabe}}
50 50  
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 +
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 |
58 +{{/aufgabe}}
59 +
60 +{{aufgabe id="Aussagen Polynomfunktion" afb="I" kompetenzen="" quelle="KMap" cc="BY-SA" zeit="3"}}
61 +Prüfe die Aussagen! Welche sind wahr? Eine Polynomfunktion 3. Grades ..
62 +☐ hat immer zwei Extrempunkte!
63 +☐ kann auch mal nur einen Extrempunkt haben!
64 +☐ kann auch mal keinen Extrempunkt haben!
65 +☐ hat immer genau einen Wendepunkt!
66 +☐ hat entweder einen Sattelpunkt oder zwei Extrempunkte!
67 +{{/aufgabe}}
68 +
69 +{{aufgabe id="Aussagen Sattelstelle" afb="I" kompetenzen="" quelle="KMap" cc="BY-SA" zeit="3"}}
70 +Welche Aussagen treffen auf eine Sattelstelle zu?
71 +☐ Eine Sattelstelle hat eine waagrechte Asymptote
72 +☐ An einer Sattelstelle hat die Steigung ein Maximum oder ein Minimum
73 +☐ An einer Sattelstelle gibt es immer auch einen Krümmungswechsel
74 +☐ Eine Sattelstelle ist auch eine Wendestelle
75 +☐ Eine Sattelstelle kann auch eine Maximalstelle sein
76 +{{/aufgabe}}
77 +
51 51  {{seitenreflexion bildungsplan="" kompetenzen="" anforderungsbereiche="" kriterien="" menge=""/}}
Aussagen.ggb
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Inhalt
Aussagen.svg
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Author
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393 +<clipPath id="clip55dea87b-6844-4194-8fd3-f87d57f4ffce">
394 + <path d="M 0.0000 0.0000 L 0.0000 361.00 L 395.00 361.00 L 395.00 0.0000 z"/>
395 +</clipPath>
396 +<g clip-path="url(#clip48)">
397 +<g stroke-linejoin="round" stroke-linecap="round" fill="none" stroke-opacity=".23529" stroke="#c0c0c0">
398 + <path d="M 0.0000 305.61 L 395.00 305.61"/>
399 +</g> <!-- drawing style -->
400 +</g> <!-- clip48 -->
401 +<clipPath id="clip9c3c3adc-5e1a-4384-ba6d-333db24a9c00">
402 + <path d="M 0.0000 0.0000 L 0.0000 361.00 L 395.00 361.00 L 395.00 0.0000 z"/>
403 +</clipPath>
404 +<g clip-path="url(#clip49)">
405 +<g stroke-linejoin="round" stroke-linecap="round" fill="none" stroke-opacity=".23529" stroke="#c0c0c0">
406 + <path d="M 0.0000 320.64 L 395.00 320.64"/>
407 +</g> <!-- drawing style -->
408 +</g> <!-- clip49 -->
409 +<clipPath id="clipf9f96851-1b90-43d5-8597-4cfd565932c3">
410 + <path d="M 0.0000 0.0000 L 0.0000 361.00 L 395.00 361.00 L 395.00 0.0000 z"/>
411 +</clipPath>
412 +<g clip-path="url(#clip50)">
413 +<g stroke-linejoin="round" stroke-linecap="round" fill="none" stroke-opacity=".23529" stroke="#c0c0c0">
414 + <path d="M 0.0000 350.69 L 395.00 350.69"/>
415 +</g> <!-- drawing style -->
416 +</g> <!-- clip50 -->
417 +<clipPath id="clip189c7617-ec9d-4d73-a762-a88b59b40a48">
418 + <path d="M 0.0000 0.0000 L 0.0000 361.00 L 395.00 361.00 L 395.00 0.0000 z"/>
419 +</clipPath>
420 +<g clip-path="url(#clip51)">
421 +<g stroke-width="2.0000" stroke-linecap="butt" fill="none" stroke-opacity="1.0000" stroke="#000000">
422 + <path d="M 195.98 3.0000 L 195.98 361.00"/>
423 +</g> <!-- drawing style -->
424 +</g> <!-- clip51 -->
425 +<clipPath id="clipdfd20443-3d9b-4e06-99fb-eac45df92aaa">
426 + <path d="M 0.0000 0.0000 L 0.0000 361.00 L 395.00 361.00 L 395.00 0.0000 z"/>
427 +</clipPath>
428 +<g clip-path="url(#clip52)">
429 +<g stroke-width="2.0000" stroke-linecap="butt" fill="none" stroke-opacity="1.0000" stroke="#000000">
430 + <path d="M 195.98 2.0000 L 190.98 7.0000"/>
431 +</g> <!-- drawing style -->
432 +</g> <!-- clip52 -->
433 +<clipPath id="clipd6047479-a44f-44ee-b8c0-631962f19619">
434 + <path d="M 0.0000 0.0000 L 0.0000 361.00 L 395.00 361.00 L 395.00 0.0000 z"/>
435 +</clipPath>
436 +<g clip-path="url(#clip53)">
437 +<g stroke-width="2.0000" stroke-linecap="butt" fill="none" stroke-opacity="1.0000" stroke="#000000">
438 + <path d="M 195.98 2.0000 L 200.98 7.0000"/>
439 +</g> <!-- drawing style -->
440 +</g> <!-- clip53 -->
441 +<clipPath id="clipeaa1df8f-de71-45d9-8acd-7a7b2c0417d6">
442 + <path d="M 0.0000 0.0000 L 0.0000 361.00 L 395.00 361.00 L 395.00 0.0000 z"/>
443 +</clipPath>
444 +<g clip-path="url(#clip54)">
445 +<g stroke-width="2.0000" stroke-linecap="butt" fill="none" stroke-opacity="1.0000" stroke="#000000">
446 + <path d="M 0.0000 185.40 L 392.00 185.40"/>
447 +</g> <!-- drawing style -->
448 +</g> <!-- clip54 -->
449 +<clipPath id="clip2ecff272-cff0-42c2-875f-fd9389567acb">
450 + <path d="M 0.0000 0.0000 L 0.0000 361.00 L 395.00 361.00 L 395.00 0.0000 z"/>
451 +</clipPath>
452 +<g clip-path="url(#clip55)">
453 +<g stroke-width="2.0000" stroke-linecap="butt" fill="none" stroke-opacity="1.0000" stroke="#000000">
454 + <path d="M 393.00 185.40 L 388.00 180.40"/>
455 +</g> <!-- drawing style -->
456 +</g> <!-- clip55 -->
457 +<clipPath id="clipe1744b1d-6aea-4e24-86aa-bf843f757102">
458 + <path d="M 0.0000 0.0000 L 0.0000 361.00 L 395.00 361.00 L 395.00 0.0000 z"/>
459 +</clipPath>
460 +<g clip-path="url(#clip56)">
461 +<g stroke-width="2.0000" stroke-linecap="butt" fill="none" stroke-opacity="1.0000" stroke="#000000">
462 + <path d="M 393.00 185.40 L 388.00 190.40"/>
463 +</g> <!-- drawing style -->
464 +</g> <!-- clip56 -->
465 +<clipPath id="clip0b4fef2e-963c-451c-b935-13469bab3afb">
466 + <path d="M 0.0000 0.0000 L 0.0000 361.00 L 395.00 361.00 L 395.00 0.0000 z"/>
467 +</clipPath>
468 +<g clip-path="url(#clip57)">
469 +<g transform="matrix(1.0000, 0.0000, 0.0000, 1.0000, 34.000, 201.00)">
470 +<text fill-opacity="1.0000" font-style="normal" font-family="Helvetica" font-weight="bold" stroke="none" fill="#000000" font-size="12.000" x="0" y="0">&#x2013;2</text>
471 +</g> <!-- transform -->
472 +</g> <!-- clip57 -->
473 +<clipPath id="clip15b2c9c1-eef3-4a8f-8a19-322470a9d215">
474 + <path d="M 0.0000 0.0000 L 0.0000 361.00 L 395.00 361.00 L 395.00 0.0000 z"/>
475 +</clipPath>
476 +<g clip-path="url(#clip58)">
477 +<g transform="matrix(1.0000, 0.0000, 0.0000, 1.0000, 112.00, 201.00)">
478 +<text fill-opacity="1.0000" font-style="normal" font-family="Helvetica" font-weight="bold" stroke="none" fill="#000000" font-size="12.000" x="0" y="0">&#x2013;1</text>
479 +</g> <!-- transform -->
480 +</g> <!-- clip58 -->
481 +<clipPath id="clip02398292-8a54-4627-87d4-5c2ec7424484">
482 + <path d="M 0.0000 0.0000 L 0.0000 361.00 L 395.00 361.00 L 395.00 0.0000 z"/>
483 +</clipPath>
484 +<g clip-path="url(#clip59)">
485 +<g transform="matrix(1.0000, 0.0000, 0.0000, 1.0000, 271.00, 201.00)">
486 +<text fill-opacity="1.0000" font-style="normal" font-family="Helvetica" font-weight="bold" stroke="none" fill="#000000" font-size="12.000" x="0" y="0">1</text>
487 +</g> <!-- transform -->
488 +</g> <!-- clip59 -->
489 +<clipPath id="clipf0174c39-5700-4b36-b891-68f2dc35c81b">
490 + <path d="M 0.0000 0.0000 L 0.0000 361.00 L 395.00 361.00 L 395.00 0.0000 z"/>
491 +</clipPath>
492 +<g clip-path="url(#clip60)">
493 +<g transform="matrix(1.0000, 0.0000, 0.0000, 1.0000, 348.00, 201.00)">
494 +<text fill-opacity="1.0000" font-style="normal" font-family="Helvetica" font-weight="bold" stroke="none" fill="#000000" font-size="12.000" x="0" y="0">2</text>
495 +</g> <!-- transform -->
496 +</g> <!-- clip60 -->
497 +<clipPath id="clip926787fe-ea86-4ffc-b518-55a6ffa82335">
498 + <path d="M 0.0000 0.0000 L 0.0000 361.00 L 395.00 361.00 L 395.00 0.0000 z"/>
499 +</clipPath>
500 +<g clip-path="url(#clip61)">
501 +<g transform="matrix(1.0000, 0.0000, 0.0000, 1.0000, 176.00, 340.00)">
502 +<text fill-opacity="1.0000" font-style="normal" font-family="Helvetica" font-weight="bold" stroke="none" fill="#000000" font-size="12.000" x="0" y="0">&#x2013;4</text>
503 +</g> <!-- transform -->
504 +</g> <!-- clip61 -->
505 +<clipPath id="clip1563c83a-c95c-4f59-9dad-282c08d30e8f">
506 + <path d="M 0.0000 0.0000 L 0.0000 361.00 L 395.00 361.00 L 395.00 0.0000 z"/>
507 +</clipPath>
508 +<g clip-path="url(#clip62)">
509 +<g transform="matrix(1.0000, 0.0000, 0.0000, 1.0000, 176.00, 265.00)">
510 +<text fill-opacity="1.0000" font-style="normal" font-family="Helvetica" font-weight="bold" stroke="none" fill="#000000" font-size="12.000" x="0" y="0">&#x2013;2</text>
511 +</g> <!-- transform -->
512 +</g> <!-- clip62 -->
513 +<clipPath id="clipc87d74ca-8757-4a23-8590-64fe5bc00cf9">
514 + <path d="M 0.0000 0.0000 L 0.0000 361.00 L 395.00 361.00 L 395.00 0.0000 z"/>
515 +</clipPath>
516 +<g clip-path="url(#clip63)">
517 +<g transform="matrix(1.0000, 0.0000, 0.0000, 1.0000, 182.00, 115.00)">
518 +<text fill-opacity="1.0000" font-style="normal" font-family="Helvetica" font-weight="bold" stroke="none" fill="#000000" font-size="12.000" x="0" y="0">2</text>
519 +</g> <!-- transform -->
520 +</g> <!-- clip63 -->
521 +<clipPath id="clipe16ba967-38e4-4433-aea8-72926fbce3f1">
522 + <path d="M 0.0000 0.0000 L 0.0000 361.00 L 395.00 361.00 L 395.00 0.0000 z"/>
523 +</clipPath>
524 +<g clip-path="url(#clip64)">
525 +<g transform="matrix(1.0000, 0.0000, 0.0000, 1.0000, 182.00, 40.000)">
526 +<text fill-opacity="1.0000" font-style="normal" font-family="Helvetica" font-weight="bold" stroke="none" fill="#000000" font-size="12.000" x="0" y="0">4</text>
527 +</g> <!-- transform -->
528 +</g> <!-- clip64 -->
529 +<clipPath id="clipe3409062-91a3-43bc-9e33-de4d0954404f">
530 + <path d="M 0.0000 0.0000 L 0.0000 361.00 L 395.00 361.00 L 395.00 0.0000 z"/>
531 +</clipPath>
532 +<g clip-path="url(#clip65)">
533 +<g transform="matrix(1.0000, 0.0000, 0.0000, 1.0000, 182.00, 201.00)">
534 +<text fill-opacity="1.0000" font-style="normal" font-family="Helvetica" font-weight="bold" stroke="none" fill="#000000" font-size="12.000" x="0" y="0">0</text>
535 +</g> <!-- transform -->
536 +</g> <!-- clip65 -->
537 +<g id="misc">
538 +</g><!-- misc -->
539 +<g id="layer0">
540 +<clipPath id="clipaca1c80e-8e88-4f30-986b-bb0797fd488b">
541 + <path d="M 0.0000 0.0000 L 0.0000 361.00 L 395.00 361.00 L 395.00 0.0000 z"/>
542 +</clipPath>
543 +<g clip-path="url(#clip66)">
544 +<g stroke-linejoin="round" stroke-width="3.5000" stroke-linecap="round" fill="none" stroke-opacity=".74902" stroke="#009900">
545 + <path d="M 61.719 -8.6233 L 63.262 -2.0105 L 64.805 4.4503 L 66.348 10.761 L 67.891 16.923 L 69.434 22.939 L 70.977 28.809 L 72.520 34.536 L 74.062 40.123 L 75.605 45.569 L 77.148 50.877 L 78.691 56.050 L 80.234 61.088 L 83.320 70.768 L 86.406 79.933 L 89.492 88.595 L 92.578 96.770 L 95.664 104.47 L 98.750 111.71 L 101.84 118.51 L 104.92 124.87 L 108.01 130.82 L 111.09 136.37 L 114.18 141.52 L 117.27 146.30 L 120.35 150.72 L 123.44 154.80 L 126.52 158.54 L 129.61 161.96 L 132.70 165.08 L 135.78 167.91 L 138.87 170.47 L 141.95 172.76 L 145.04 174.80 L 148.12 176.62 L 151.21 178.21 L 154.30 179.60 L 157.38 180.79 L 160.47 181.81 L 163.55 182.67 L 166.64 183.38 L 169.73 183.95 L 172.81 184.41 L 175.90 184.75 L 178.98 185.01 L 182.07 185.19 L 185.16 185.30 L 188.24 185.37 L 191.33 185.39 L 194.41 185.40 L 197.50 185.40 L 200.59 185.41 L 203.67 185.44 L 206.76 185.50 L 209.84 185.62 L 212.93 185.79 L 216.02 186.05 L 219.10 186.39 L 222.19 186.85 L 225.27 187.42 L 228.36 188.12 L 231.45 188.98 L 234.53 190.00 L 237.62 191.19 L 240.70 192.57 L 243.79 194.16 L 246.88 195.97 L 249.96 198.01 L 253.05 200.30 L 256.13 202.85 L 259.22 205.68 L 262.30 208.79 L 265.39 212.21 L 268.48 215.95 L 271.56 220.02 L 274.65 224.43 L 277.73 229.21 L 280.82 234.36 L 283.91 239.90 L 286.99 245.84 L 290.08 252.20 L 293.16 258.99 L 296.25 266.22 L 299.34 273.92 L 302.42 282.08 L 305.51 290.74 L 308.59 299.89 L 311.68 309.57 L 313.22 314.60 L 314.77 319.77 L 316.31 325.07 L 317.85 330.52 L 319.39 336.10 L 320.94 341.82 L 322.48 347.69 L 324.02 353.70 L 325.57 359.86 L 327.11 366.16"/>
546 +<title>Function g</title>
547 +<desc>g(x) = -x³</desc>
548 +
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550 +</g> <!-- clip66 -->
551 +</g><!-- layer0 -->
552 +<defs>
553 +<font id="Helvetica" horiz-adv-x="0" >
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555 +<missing-glyph d=""/>
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559 +<glyph unicode="&#x0030;" horiz-adv-x="57.195" d="M 53.500 35.703 Q 53.500 24.203 51.047 16.000 Q 48.594 7.7969 43.148 3.3984 Q 37.703 -1.0000 28.500 -1.0000 Q 15.594 -1.0000 9.5938 8.7500 Q 3.5938 18.500 3.5938 35.703 Q 3.5938 47.297 6.0000 55.500 Q 8.4062 63.703 13.906 68.102 Q 19.406 72.500 28.500 72.500 Q 41.297 72.500 47.398 62.797 Q 53.500 53.094 53.500 35.703 z M 18.594 35.703 Q 18.594 23.500 20.695 17.352 Q 22.797 11.203 28.500 11.203 Q 34.094 11.203 36.297 17.305 Q 38.500 23.406 38.500 35.703 Q 38.500 47.906 36.297 54.102 Q 34.094 60.297 28.500 60.297 Q 22.797 60.297 20.695 54.102 Q 18.594 47.906 18.594 35.703 z"/>
560 +<glyph unicode="&#x2013;" horiz-adv-x="49.995" d="M 4.0000 21.297 L 4.0000 32.500 L 46.000 32.500 L 46.000 21.297 L 4.0000 21.297 z"/>
561 +</font>
562 +
563 +</defs> <!-- font definitions -->
564 +</g> <!-- default stroke -->
565 +</svg> <!-- bounding box -->
566 +