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Lineare und ganzrationale Funktionen für die gymnasiale Mittel- und Oberstufe

Lineare und ganzrationale Funktionen für die gymnasiale Mittel- und Oberstufe

          
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About the Book

Skript aus dem Jahr 2011 im Fachbereich Mathematik - Algebra, Sprache: Deutsch, Abstract: [...] Die violette Kurve f(x) beschreibt die Funktion, nach der ein Becken mit Wasser gefüllt wird. Sie beschreibt die zugeführte Menge an Wasser. Da die Kurve keine Steigung hat, bleibt auch die Zufuhr der Wassermenge konstant. Geht man davon aus, dass zu Beginn noch kein Wasser im Becken war, kann man annehmen, dass die rote Kurve den Wasserbestand im Becken beschreibt. Die Steigung der Kurve ist 1. Das heißt, dass pro Einheit eins dazu kommt. Wer genau hinschaut merkt: Die violette Kurve ist die Ableitung der roten Kurve. Klar, die violette Kurve ist die Änderung des Bestandes, der mit der roten Kurve beschrieben wird. Man spricht davon, dass die rote Kurve eine Stammfunktion der violetten Kurve ist. Möchte man nun herausfinden, wie groß der Wasserbestand nach 6 Stunden ist, so muss man einfach den Funktionswerte der Stammfunktion bei x=6 nehmen. Wenn jede Stunde 1 m3 Wasser hinzu kommt, sind es nach 6 Stunden 6m3 - der Funktionswert der Stammfunktion. In der unteren Abbildung ist die steigende Gerade um 2 nach oben verschoben. Das heißt, dass der Wasserbestand zu Beginn schon bei 2m3 lag. Aber auch die Ableitung der roten Funktion ist die violette Funktion - der Zahlenwert +2 fällt beim Differenzieren ja weg. Also hat die violette Kurve jetzt schon zwei Stammfunktionen - und es gibt noch unendlich viele mehr, je nachdem, welchen Wert man als Anfangsbestand festlegt. Das nächste Beispiel beschreibt die Höhenänderung bei einem Heißluftballonflug: Zu Beginn hat der Heißluftballon noch keine Höhenänderung - denn der Wert bei x=0 ist null. Ab dort steigt der Ballon allerdings weiter, bis er am Hochpunkt der Funktion seine Höchste Steigung hat. Doch Achtung: nach dem Hochpunkt sinkt der Ballon nicht! Er hat nur eine geringere Höhenänderung als davor. Bis zur Nullstelle der Funktion steigt der Ballon. Bei der Nullstelle bleibt der Ballon stehen, ab dann sinkt er. Beim Tiefpunkt


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Product Details
  • ISBN-13: 9783640943654
  • Publisher: Grin Publishing
  • Binding: Paperback
  • Language: German
  • Returnable: N
  • Spine Width: 5 mm
  • Width: 148 mm
  • ISBN-10: 3640943651
  • Publisher Date: 13 Jul 2011
  • Height: 210 mm
  • No of Pages: 84
  • Series Title: German
  • Weight: 122 gr


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