Streckung und Stauchung von Graphen

Question

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.

Answer 1

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.

Comments

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.

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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

TRANSLATE with x English

Arabic	Hebrew	Polish
Bulgarian	Hindi	Portuguese
Catalan	Hmong Daw	Romanian
Chinese Simplified	Hungarian	Russian
Chinese Traditional	Indonesian	Slovak
Czech	Italian	Slovenian
Danish	Japanese	Spanish
Dutch	Klingon	Swedish
English	Korean	Thai
Estonian	Latvian	Turkish
Finnish	Lithuanian	Ukrainian
French	Malay	Urdu
German	Maltese	Vietnamese
Greek	Norwegian	Welsh
Haitian Creole	Persian

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'; TRANSLATE with COPY 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 --> Back EMBED THE SNIPPET BELOW IN YOUR SITE 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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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.

Answer 2

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

Comments

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 x English

Arabic	Hebrew	Polish
Bulgarian	Hindi	Portuguese
Catalan	Hmong Daw	Romanian
Chinese Simplified	Hungarian	Russian
Chinese Traditional	Indonesian	Slovak
Czech	Italian	Slovenian
Danish	Japanese	Spanish
Dutch	Klingon	Swedish
English	Korean	Thai
Estonian	Latvian	Turkish
Finnish	Lithuanian	Ukrainian
French	Malay	Urdu
German	Maltese	Vietnamese
Greek	Norwegian	Welsh
Haitian Creole	Persian

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'; TRANSLATE with COPY 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 --> Back EMBED THE SNIPPET BELOW IN YOUR SITE 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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Sag mal, benutzt du irgendein Übersetzungsprogram, zum Beispiel den Bing Translator?

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

TRANSLATE with x English

Arabic	Hebrew	Polish
Bulgarian	Hindi	Portuguese
Catalan	Hmong Daw	Romanian
Chinese Simplified	Hungarian	Russian
Chinese Traditional	Indonesian	Slovak
Czech	Italian	Slovenian
Danish	Japanese	Spanish
Dutch	Klingon	Swedish
English	Korean	Thai
Estonian	Latvian	Turkish
Finnish	Lithuanian	Ukrainian
French	Malay	Urdu
German	Maltese	Vietnamese
Greek	Norwegian	Welsh
Haitian Creole	Persian

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'; TRANSLATE with COPY 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 --> Back EMBED THE SNIPPET BELOW IN YOUR SITE 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);