Verhalten für x nahe 0

[color=#ff0000][b]Merksatz: Für x nahe 0 wird das Verhalten einer ganzrationalen Funktion f(x)[/b][/color][b][color=#ff0000] von dem Summanden mit der niedrigsten Potenz von x bestimmt.[/color][br][/b] [u]Bemerkung:[/u] Das absolute Glied muss in die Betrachtung einbezogen werden.[br][br][u][b][size=150]Beispiel[/size][/b][/u][br]Gegeben ist die Funktion [math]f\left(x\right)=x^3+x^2-5x+2[/math]. Wird in dem untenstehenden Fenster auf die Stelle f(0) hereingezoomt, ist erkenntlich, dass der Graph, je genauer der Ausschnitt wird, immer mehr einer Geraden ähnelt.[br][br]Zoome mit dem Mausrad auf die Stelle f(0)=2 und beobachte das oben Beschriebene.[br][br]Aktiviere nun den Graphen der Geraden g(x)=-5x + 2 (klick auf den Kreis neben g(x)). Wird hinreichend nah an f(0) herangeszoomed sind f(x) und g(x) (nahezu) deckungsgleich.[br]Der Graph von f(x) für x nahe Null, d.h. Nahe dem Wert f(0), verhält sich somit wie der Graph der Gerade g(x)=-5x+2. [br]Also verhält sich der Graph von [math]f\left(x\right)=x^3+x^2-5x+2[/math] nahe Null wie der Summand von f(x) mit der niedrigsten Potenz von x (das absolute Glied eingeschlossen).
[b]Beispiel 2.[/b][br][br]Der Graph der Funktion [math]f\left(x\right)=-5x^5+2x^4+2x^2-3[/math] verhält sich für x nahe 0 wie [math]g\left(x\right)=2x^2-3[/math], also wie der Summand mit der niedrigsten Potenz von x (siehe Graph).

Verhalten für x → ±∞

[color=#ff0000][b]Merksatz: Für x → ±∞ wird das Verhalten einer ganzrationalen Funktion f(x) [/b][b]von dem Summanden mit der höchsten Potenz von x bestimmt. [/b][/color][br][br][br]Dieses wird an folgendem Beispiel deutlich:[br]Gegeben ist die Funktion [math]f\left(x\right)=x^3-100x^2-100x-100[/math]. Mit Hilfe des Schiebereglers kann man den x-Wert sehr groß bzw. sehr klein werden lassen.
Welche Aussagen stimmen für die Funktion [math]f\left(x\right)=x^3-100x^2-100x-100[/math]
Tipp 1
Das [b]Verhalten für unendlich große x-Werte[/b] (bzw. kleine bei negativem x) wird also von dem [b]Summanden[/b] mit dem [b]größten Exponenten bestimmt[/b]. In dem obigen Beispiel muss demnach nur [math]g\left(x\right)=x^3[/math] betrachtet werden.[br][br]In dem Beispiel sorgt [math]g\left(x\right)=x^3[/math]dafür, dass für [color=#ff0000]große x[/color] die [color=#ff0000]Funktionswerte von f(x) positiv unendlich[/color] werden (eine positive Zahl "hoch 3" ist positiv). Und für [color=#38761d]kleine x[/color] sorgt der Term dafür, dass die [color=#38761d]Funktionswerte von f(x) negativ unendlich[/color] werden (eine negative Zahl "hoch 3" ist negativ).
Betrachten wir abschließend die Funktion [math]f\left(x\right)=-2x^4+8x^3+3x-2[/math].
Die Funktion [math]f\left(x\right)=-2x^4+8x^3+3x-2[/math] verhält sich für x → ±∞ wie die Funktion ................. .
Das bedeutet für [math]f\left(x\right)=-2x^4+8x^3+3x-2[/math] gilt:
Tipp 2
Das heißt, dass der Graph von f [color=#38761d]auf der linken [/color][math]\left(x\rightarrow-\infty\right)[/math] und [color=#ff0000]auf der rechten Seite [/color][math]\left(x\rightarrow+\infty\right)[/math] jeweils nach [math]-\infty[/math], d.h. nach unten geht. Dies zeigt auch die folgende Abbildung der Funktion.

Symmetrie ganzrationaler Funktionen

[color=#ff0000][b]Merksatz:[/b][br]Der Graph einer Funktion f ist genau dann [/color][list][*][color=#ff0000][b][u]achsensymmetrisch zur y-Achs[/u][u]e[/u][/b]    [/color][/*][/list][color=#ff0000]  wenn für alle x-Werte aus dem Definitionsbereich gilt, dass [b]f(-x) = f(x)[/b].[/color][br]  Diese Bedingung ist erfüllt, wenn f(x) [b]nur Potenzen mit geraden Exponenten enthält. [/b][br]   (Achtung Exponent bei absolutem Glied (b) ist gerade! [math]x^0\cdot b=1\cdot b=b[/math]) [br][br][list][*][color=#ff0000][u][b]pu[/b][/u][b][u]nktsymmetrisch zum Ursprung[/u][/b] (0|0)[/color][/*][/list][color=#ff0000]  wenn für alle x-Werte aus dem Definitionsbereich gilt, dass [b]f(-x) = -f(x)[/b][/color][br]  Diese Bedingung ist erfüllt, wenn f(x) [b]nur Potenzen mit ungeraden Exponenten enthält.[/b](Achtung x hat den Exponenten 1 und ist somit ungerade! [math]x^1=x[/math])[br][br]-->[u] Vorgehen bei der rechnerischen Überprüfung auf Symmetrie:[/u] -x in f(x) einsetzen, umformen und mit f(x) vergleichen. [br][br][b][u]Hinweis:[/u][/b] beinhaltet der Funktionsterm einer Funktion f(x) [b]sowohl gerade als auch ungerade Potenzen[/b] ist der Graph [b]weder Achsensymmetrisch zur y-Achse noch Punktsymmetrisch zum Ursprung![br][/b]
Achsensymmetrie
Punktsymmetrie
[b]Beispiel Achsensymmetrie:[/b][br]der Graph der Funktion [math]f\left(x\right)=4x^6-3x^2+0,4[/math] ist achsensymmetrisch zur y-Achse, da der Term nur gerade Exponenten enthält.[br]Rechnerisch kann dies so gezeigt werden:[br][math]f\left(-x\right)=4\left(-x\right)^6-3\left(-x\right)^2+0,4=4x^6-3x^2+0,4=f\left(x\right)[/math]
[b]Beispiel Punktsymmetrie:[/b][br]der Graph der Funktion [math]g\left(x\right)=-7x^5+2x^3-4x[/math] ist punktsymmetrisch zum Ursprung, da der Term nur ungerade Exponenten enthält.[br]Rechnerisch kann dies so gezeigt werden:[br][math]g\left(-x\right)=-7\left(-x\right)^5+2\left(-x\right)^3-4\left(-x\right)=7x^5-2x^3+4x=-\left(-7x^5+2x^3-4x\right)=-g\left(x\right)[/math]
Die Graphen der Funktionen h und k sind weder achsensymmetrisch zur y-Achse, noch Punktsymmetrisch zum Ursprung:[br][list][*]da für [math]h\left(x\right)=4x^4+2x^2+3x[/math] sowohl gerade als auch ungerade ([math]x^1=x[/math]) Exponenten vorkommen[/*][*]da für [math]k\left(x\right)=x^5+3x^3-2x+2[/math] sowohl ungerade als auch gerade ([math]2=2x^0=2\cdot1[/math]) vorkommen.[br][/*][/list]

Nullstellen allgemein

Was ist eine Nullstelle?
Ein Element [math]x_0[/math] aus der Definitionsmenge einer Funktion f([math]x[/math]) heißt [b]Nullstelle (NST), wenn gilt: [/b][math]f\left(x_0\right)=0[/math]. Nullstellen sind somit die [b]x-Werte einer Funktion für die die Funktion den Wert 0 annimmt[/b], der Graph also die x-Achse schneidet.[br][br][img]data:image/png;base64,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[/img][br][br]Eine [b]ganzrationale Funktion vom Grad n[/b] kann [b]höchstens n Nullstellen[/b] haben. [br]Über die Funktion [math]h\left(x\right)=3x^4-2x^3+2x+2[/math] wissen wir somit, dass sie [u]höchstens[/u] 4 Nullstellen haben kann.[br]Über die Funktion [math]k\left(x\right)=100x^3-2x^2+4[/math] wissen wir somit, dass sie [u]höchstens[/u] 3 Nullstellen haben kann.[br] Wichtig: es können natürlich auch weniger NST sein.
Nullstellen haben bei Anwendungsaufgaben häufig eine besondere Bedeutung. So könnte im Beispiel unten gefragt werden, wie weit die Kugelstoßerin die Kugel stößt. Gesucht wäre in diesem Fall die Distanz von dem Abstoßpunkt ([math]x_1=0[/math]) bis zum Auftreffen der Kugel ([math]x_2=?[/math]). [math]x_2[/math] ist hier die gesuchte Nullstelle.[br][br][img]data:image/png;base64,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[/img]
Nullstellen von quadratischen Funktionen (Funktionen vom Grad 2) können mithilfe der pq-Formel bestimmt werden.[br][math]x_{1,2}=-\frac{p}{2}\pm\sqrt{\left(\frac{p}{2}\right)^2-q}[/math]
[b]Für das Bestimmen der NST von ganzrationalen Funktionen mit höherem Grad gibt es [u]drei nützliche Verfahren[/u]: [u]Ablesen, Ausklammern und Substitution[/u]. [br]Diese sind in den nächsten drei Kapiteln beschrieben.[/b]

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