Schnittstellen mit den Koordinatenachsen

Schnittstellen mit der x-Achse
Einen x-Wert, bei dem der Graph einer Funktion die x-Achse schneidet, nennt man eine [b][i]Nullstelle der Funktion[/i][/b].[br][br][img]data:image/png;base64,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[/img][br][br]Die Nullstellen der oben abgebildete Funktionen lauten x[sub]1[/sub] = 1 und x[sub]2[/sub] = 3.[br][br][b]Warum der Name [i]Nullstelle[/i]?[/b][br]Weil bei einem x-Wert, bei dem der Graph die x-Achse schneidet, der Funktionswert gleich 0 ist! [br]Der Graph verläuft nämlich dort, wo er die x-Achse schneidet, auf der Höhe von y = 0. Das wiederum bedeutet, dass bei diesem x-Wert der Funktionswert gleich 0 ist.[br][br]Es gilt also: [b]für x[sub]1[/sub] ist f(x[sub]1[/sub]) = 0 <=> x[sub]1[/sub] ist Nullstelle der Funktion f [/b] [br][br][b]Nullstellen berechnen[/b][br]Mit dieser Erkenntnis kann man leicht berechnen, "was die Nullstellen einer Funktion sind", d.h. bei welchen x-Werten der Graph der Funktion die x-Achse schneidet.[br][br]Angenommen die Funktion lautet f(x) = 4x – 1.[br]Die Nullstellen der Funktion f sind die x-Werte, für die [br] f(x) = 0 ist, [br]d.h. für die 4x – 1 = 0 ist.[br]Wir lösen die Gleichung nach x auf und erhalten:[br] 4x = 1[br] x = 0,25[br][br]Die Funktion f(x) = 4x – 1 hat also eine Nullstelle und zwar bei x = 0,25.
Aufgabe
Gegeben ist die Funktion [math]f\left(x\right)=x^2-4[/math][br]Bestimmen Sie die Nullstellen der Funktion.
Lösung
Die Nullstellen der Funktion sind die Lösungen der Gleichung f(x) = 0.[br]d.h. hier der Gleichung [math]x^2-4=0[/math][br]Umformen ergibt: [math]x^2=4[/math][br]Diese Gleichung hat zwei Lösungen: [math]x_1=-2[/math] und [math]x_2=2[/math].[br][br]Die Funktion hat damit zwei Nullstellen: [math]x_1=-2;x_2=2[/math]. [br]Hier der Graph der Funktion:[br][img]data:image/png;base64,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[/img]
Aufgabe
Bestimmen Sie die Nullstellen der Funktion [math]f\left(x\right)=\frac{1}{x}[/math] .
Lösung
Die Berechnung der Nullstellen führt auf die Gleichung [math]\frac{1}{x}=0[/math][br]Diese Gleichung hat keine Lösung![br]D.h. die Funktion schneidet die x-Achse nicht.[br]Das zeigt sich am Graphen:[br][img]data:image/png;base64,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[/img][br]Der Graph nähert sich für wachsende x-Wert zwar immer näher der x-Achse an, erreicht sie aber nie, da der Term 1/x auch für noch so grosse x-Wert immer einen Wert grösser als 0 besitzt.
Schnittstellen mit der y-Achse
Die Stelle, bei der der Graph einer Funktion die y-Achse schneidet, kann man leicht bestimmen![br]Sie ist nämlich gleich der Höhe des Graphen x = 0 und ist damit gleich dem Funktionswert bei x = 0.[br][br]Es gilt also:[br] [b]Schnittstelle mit der y-Achse = f(0)[/b][br][br]Wir berechnen, wo die Funktion f(x) = 4x – 1 die y-Achse schneidet.[br][br]Schnittstelle mit der y-Achse = f(0) = 4·0 – 1 = 0 – 1 = –1.[br][br]Der Graph der Funktion f(x) = 4x – 1 schneidet die y-Achse also bei y = –1.
Aufgabe
Gegeben ist die Funktion [math]f\left(x\right)=x^2-4[/math][br]Wo schneidet der Graph die y-Achse?
Lösung
Die Schnittstelle mit der y-Achse ist gleich dem Funtionswert bei x = 0:[br]Schnittstelle mit y-Achse = [math]f\left(0\right)=0^2-4=0-4=-4[/math]
Aufgabe
Bestimmen Sie für die Funktion [math]f\left(x\right)=\frac{1}{x}[/math] die Schnittstelle mit der y-Achse.[br]
Lösung
Die Berechnung der Schnittstelle mit der y-Achse führt auf die Berechnung:[br]Schnittstelle mit der y-Achse = [math]f\left(0\right)=\frac{1}{0}[/math][br]Die Division durch 0 ist nicht definiert: d.h. es gibt keine Schnittstelle mit der y-Achse.[br]Das zeigt sich am Graphen: [br][img]data:image/png;base64,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[/img][br]Je nach dem von welcher Seite man sich der Stelle x = 0 nähert, strebt der der Funktionswert gegen minus oder plus unendlich: Für x = 0 ist kein Funktionswert ermittelbar.
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Informatie: Schnittstellen mit den Koordinatenachsen