0 Daumen
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Aufgabe:

Die Graphen von f1, f2, f3 sind aus dem Graphen von f entstanden.


Problem/Ansatz:

Ich soll die zugehörigen Funktionsgleichungen für die Funktionen f1, f2 und f3 angeben, aber ich komme nicht weiter.

Könnt ihr mir bitte erklären, wie man systematisch diese Fragen lösen soll.


Meine Frage:

Wie kann kann unterscheiden zwischen Streckung bzw. Stauchung von den Graphen nur beim Anschauen der Graphen.

von

2 Antworten

0 Daumen
 
Beste Antwort

Du hast die Originalfunktion f(x)

g(x) geht aus dem Graphen von f(x) hervor und es gilt

g(x) = a * f(b * (x + c)) + d

a ist eine Streck-Stauchung in y-Richtung und/oder eine Spiegelung an der x-Achse.

b ist eine Streck-Stauchung in x-Richtung und/oder eine Spiegelung an der y-Achse.

c ist eine Verschiebung in x-Richtung

d ist eine Verschiebung in y-Richtung

Wenn du eine detailliertere Aufgabenstellung zur Verfügung stellst, kann ich auch eine detailliertere Lösung zur Verfügung stellen.

von 388 k 🚀

Vielen Dank für deine schnelle Erklärung.

Leider kann ich das Bild nicht hochladen.

Aber kannst du mir bitte erklären, wie man unterscheidet welcher Graph gestaucht bzw. gestreckt ist, nur beim Anschauen.

Vielen Dank für deine Erklärung.

Aber wenn ich nur die Graphen haben und die Funktionstermen bestimmen muss, wie solle ich vor gehen?

Wie kann ich erkennen :

a.- ob g2 gestreckt in y-Richtung oder gestaucht in X-Richtung ist?

b.- ob g3 gestreckt in x-Richtung oder gestreckt in y-Richtung ist?

c.- die Faktoren a und b

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Aber wenn ich nur die Graphen haben und die Funktionstermen bestimmen muss, wie solle ich vor gehen?

Wie kann ich erkennen :

a.- ob g2 gestreckt in y-Richtung oder gestaucht in X-Richtung ist?

b.- ob g3 gestreckt in x-Richtung oder gestreckt in y-Richtung ist?

c.- die Faktoren a und b

Das hängt von der Funktion ab.Bei Parabeln betrachtet man nur die Streckung in y-Richtung

y = a * (x + c)^2 + d

Bei Trigonometrischen Funktionen betrachtet man aber z.B. Streckungen/Stauchungen sowohl in x als auch y-Richtung.

0 Daumen

Hallo

mach aus deinem Bild ein png oder einen screenshot.

 2. strecken und Stauchen ist mein in y Richtung gemeint, Strecken jeder Punkt der Kurve ist hinterher höher, Beispiel 2x^2 ist die um 2 Gestreckte Normalparabel,

Stauchen jeder Punkt ist hinterher niedriger: Beispiel y=1/2x^2: grün Normalparabel,  rot gestreckt, blau gestaucht.

wenn man in x Richtung staucht oder Strecke ist es genau andersrum. blau ist in x- Richtung gestreckt, rot gestaucht.

suche z.B f(1) dabb sieh nach ist f1(1) größer, wienvielfach? dann ist es gestreckt, dann noch sehen ob f(2) genau mal soviel größer ist

Gruß lul

von 65 k 🚀

Vielen Dank für deine Erklärung.

Aber es ist mir noch nicht klar mit dem Erkennen ob der Graph gestreckt oder gestaucht ist ( in x-Richtung) und die Faktoren a und b wenn man nur die Graphen bekommt.

MfG

VanLyMai

TRANSLATE with image x English
ArabicHebrewPolish
BulgarianHindiPortuguese
CatalanHmong DawRomanian
Chinese SimplifiedHungarianRussian
Chinese TraditionalIndonesianSlovak
CzechItalianSlovenian
DanishJapaneseSpanish
DutchKlingonSwedish
EnglishKoreanThai
EstonianLatvianTurkish
FinnishLithuanianUkrainian
FrenchMalayUrdu
GermanMalteseVietnamese
GreekNorwegianWelsh
Haitian CreolePersian
var LanguageMenu; var LanguageMenu_keys=["ar","bg","ca","zh-CHS","zh-CHT","cs","da","nl","en","et","fi","fr","de","el","ht","he","hi","mww","hu","id","it","ja","tlh","ko","lv","lt","ms","mt","no","fa","pl","pt","ro","ru","sk","sl","es","sv","th","tr","uk","ur","vi","cy"]; var LanguageMenu_values=["Arabic","Bulgarian","Catalan","Chinese Simplified","Chinese Traditional","Czech","Danish","Dutch","English","Estonian","Finnish","French","German","Greek","Haitian Creole","Hebrew","Hindi","Hmong Daw","Hungarian","Indonesian","Italian","Japanese","Klingon","Korean","Latvian","Lithuanian","Malay","Maltese","Norwegian","Persian","Polish","Portuguese","Romanian","Russian","Slovak","Slovenian","Spanish","Swedish","Thai","Turkish","Ukrainian","Urdu","Vietnamese","Welsh"]; var LanguageMenu_callback=function(){ }; var LanguageMenu_popupid='__LanguageMenu_popup'; image image image TRANSLATE with imageCOPY THE URL BELOW <!-- a id="TwitterLink" title="Share on Twitter"> <img id="TwitterImg" /></a> <a-- id="FacebookLink" title="Share on Facebook"> <img id="FacebookImg" /></a -->image image Back EMBED THE SNIPPET BELOW IN YOUR SITE image Enable collaborative features and customize widget: Bing Webmaster PortalBackvar intervalId = setInterval(function () { if (MtPopUpList) { LanguageMenu = new MtPopUpList(); var langMenu = document.getElementById(LanguageMenu_popupid); var origLangDiv = document.createElement("div"); origLangDiv.id = "OriginalLanguageDiv"; origLangDiv.innerHTML = "<span id='OriginalTextSpan'>ORIGINAL: </span><span id='OriginalLanguageSpan'></span>"; langMenu.appendChild(origLangDiv); LanguageMenu.Init('LanguageMenu', LanguageMenu_keys, LanguageMenu_values, LanguageMenu_callback, LanguageMenu_popupid); window["LanguageMenu"] = LanguageMenu; clearInterval(intervalId); } }, 1);

Sag mal, benutzt du irgendein Übersetzungsprogram, zum Beispiel den Bing Translator?

Auf einmal kommt dieses kommische Bild, ich versuchte es zu lösen aber es ist mir nicht gelungen.

TRANSLATE with image x English
ArabicHebrewPolish
BulgarianHindiPortuguese
CatalanHmong DawRomanian
Chinese SimplifiedHungarianRussian
Chinese TraditionalIndonesianSlovak
CzechItalianSlovenian
DanishJapaneseSpanish
DutchKlingonSwedish
EnglishKoreanThai
EstonianLatvianTurkish
FinnishLithuanianUkrainian
FrenchMalayUrdu
GermanMalteseVietnamese
GreekNorwegianWelsh
Haitian CreolePersian
var LanguageMenu; var LanguageMenu_keys=["ar","bg","ca","zh-CHS","zh-CHT","cs","da","nl","en","et","fi","fr","de","el","ht","he","hi","mww","hu","id","it","ja","tlh","ko","lv","lt","ms","mt","no","fa","pl","pt","ro","ru","sk","sl","es","sv","th","tr","uk","ur","vi","cy"]; var LanguageMenu_values=["Arabic","Bulgarian","Catalan","Chinese Simplified","Chinese Traditional","Czech","Danish","Dutch","English","Estonian","Finnish","French","German","Greek","Haitian Creole","Hebrew","Hindi","Hmong Daw","Hungarian","Indonesian","Italian","Japanese","Klingon","Korean","Latvian","Lithuanian","Malay","Maltese","Norwegian","Persian","Polish","Portuguese","Romanian","Russian","Slovak","Slovenian","Spanish","Swedish","Thai","Turkish","Ukrainian","Urdu","Vietnamese","Welsh"]; var LanguageMenu_callback=function(){ }; var LanguageMenu_popupid='__LanguageMenu_popup'; image image image TRANSLATE with imageCOPY THE URL BELOW <!-- a id="TwitterLink" title="Share on Twitter"> <img id="TwitterImg" /></a> <a-- id="FacebookLink" title="Share on Facebook"> <img id="FacebookImg" /></a -->image image Back EMBED THE SNIPPET BELOW IN YOUR SITE image Enable collaborative features and customize widget: Bing Webmaster PortalBackvar intervalId = setInterval(function () { if (MtPopUpList) { LanguageMenu = new MtPopUpList(); var langMenu = document.getElementById(LanguageMenu_popupid); var origLangDiv = document.createElement("div"); origLangDiv.id = "OriginalLanguageDiv"; origLangDiv.innerHTML = "<span id='OriginalTextSpan'>ORIGINAL: </span><span id='OriginalLanguageSpan'></span>"; langMenu.appendChild(origLangDiv); LanguageMenu.Init('LanguageMenu', LanguageMenu_keys, LanguageMenu_values, LanguageMenu_callback, LanguageMenu_popupid); window["LanguageMenu"] = LanguageMenu; clearInterval(intervalId); } }, 1);

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