Änderungen von Dokument Lösung Erkunden (eine Potenzfunktion) - Wertetabelle

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...	...	@@ -1,32 +1,28 @@
	1	+Untersuche die Funktion //f// mit {{formula}}f(x)=\frac{1}{x}{{/formula}} und Definitionsbereich {{formula}}\mathbb{R}^*{{/formula}} im Hinblick auf ihr Randverhalten und ihre Wertemenge. Ergänze dafür zunächst folgende Wertetabellen.
	2	+
1	1	(% style="list-style: alphastyle" %)
2	2	1. (((Randverhalten: Verhalten im Unendlichen
3	3	1) Verhalten gegen plus Unendlich ({{formula}}+\infty{{/formula}})
4	4	(% class="border" %)
5		-|={{formula}}x{{/formula}}| {{formula}}+1{{/formula}}| {{formula}}+10{{/formula}}| {{formula}}+100{{/formula}}| {{formula}}+1000{{/formula}}| {{formula}}+10^6{{/formula}}| {{formula}}+10^9{{/formula}}| {{formula}}+10^{12}{{/formula}}|{{formula}}+10^{+\infty}{{/formula}}
	7	+|={{formula}}x{{/formula}}| {{formula}}+1{{/formula}}| {{formula}}+10{{/formula}}| {{formula}}+100{{/formula}}| {{formula}}+1000{{/formula}}| {{formula}}+10^6{{/formula}}| {{formula}}+10^9{{/formula}}| {{formula}}+10^{12}{{/formula}}|({{formula}}+10^{+\infty}{{/formula}})
6	6	|={{formula}}f(x){{/formula}}|1|{{formula}}\frac{1}{10}{{/formula}}|{{formula}}\frac{1}{100}{{/formula}}|{{formula}}\frac{1}{1000}{{/formula}}|{{formula}}\frac{1}{1000000}{{/formula}}|{{formula}}\frac{1}{1000000000}{{/formula}}|{{formula}}\frac{1}{1000000000000}{{/formula}}|0
7	7
8	8	2) Verhalten gegen minus Unendlich ({{formula}}-\infty{{/formula}})
9	9	(% class="border" %)
10		-|={{formula}}x{{/formula}}| {{formula}}-1{{/formula}}| {{formula}}-10{{/formula}}| {{formula}}-100{{/formula}}| {{formula}}-1000{{/formula}}| {{formula}}-10^6{{/formula}}| {{formula}}-10^9{{/formula}}|{{formula}}-10^{12}{{/formula}}|{{formula}}-10^{-\infty}{{/formula}}
11		-|={{formula}}f(x){{/formula}}|{{formula}}-1{{/formula}}|{{formula}}-\frac{1}{10}{{/formula}}|{{formula}}-\frac{1}{100}{{/formula}}|{{formula}}-\frac{1}{1000}{{/formula}}|{{formula}}-\frac{1}{1000000}{{/formula}}|{{formula}}\frac{1}{1000000000}{{/formula}}|{{formula}}\frac{1}{1000000000000}{{/formula}}|0
	12	+|={{formula}}x{{/formula}}| {{formula}}-1{{/formula}}| {{formula}}-10{{/formula}}| {{formula}}-100{{/formula}}| {{formula}}-1000{{/formula}}| {{formula}}-10^6{{/formula}}| {{formula}}-10^9{{/formula}}|{{formula}}-10^{12}{{/formula}}|
	13	+|={{formula}}f(x){{/formula}}||{{formula}}-1{{/formula}}|{{formula}}-\frac{1}{100}{{/formula}}|{{formula}}-\frac{1}{1000}{{/formula}}|{{formula}}-\frac{1}{1000000}{{/formula}}|{{formula}}\frac{1}{1000000000}{{/formula}}|{{formula}}\frac{1}{1000000000000}{{/formula}}|0
12	12	)))
13	13	1. (((Randverhalten: Verhalten nahe der Definitionslücke ({{formula}}x \approx 0{{/formula}})
14	14	1) Verhalten links bei der Definitionslücke ({{formula}}x \approx 0{{/formula}} mit {{formula}}x<0{{/formula}})
15	15	(% class="border" %)
16	16	|={{formula}}x{{/formula}}| {{formula}}-1{{/formula}}| {{formula}}-0,1{{/formula}}| {{formula}}-0,01{{/formula}}| {{formula}}-0,001{{/formula}}| {{formula}}-10^{-6}{{/formula}}| {{formula}}-10^{-9}{{/formula}}| {{formula}}-10^{-12}{{/formula}}|0
17		-|={{formula}}f(x){{/formula}}|{{formula}}-1{{/formula}}|{{formula}}-10{{/formula}}|{{formula}}-100{{/formula}}|{{formula}}-1000{{/formula}}|{{formula}}-10^6{{/formula}}| {{formula}}-10^9{{/formula}}|{{formula}}-10^{-12}{{/formula}}|{{formula}}-\infty{{/formula}}
	19	+|={{formula}}f(x){{/formula}}||||||||
18	18
19	19	2) Verhalten rechts bei der Definitionslücke ({{formula}}x \approx 0{{/formula}} mit {{formula}}x>0{{/formula}})
20	20	(% class="border" %)
21	21	|={{formula}}x{{/formula}}| {{formula}}+1{{/formula}}| {{formula}}+0,1{{/formula}}| {{formula}}+0,01{{/formula}}| {{formula}}+0,001{{/formula}}| {{formula}}+10^{-6}{{/formula}}| {{formula}}+10^{-9}{{/formula}}| {{formula}}+10^{-12}{{/formula}}|0
22		-|={{formula}}f(x){{/formula}}|{{formula}}1{{/formula}}|{{formula}}10{{/formula}}|{{formula}}100{{/formula}}|{{formula}}1000{{/formula}}|{{formula}}10^6{{/formula}}| {{formula}}10^9{{/formula}}|{{formula}}10^{-12}{{/formula}}|{{formula}}\infty{{/formula}}
	24	+|={{formula}}f(x){{/formula}}||||||||
23	23	)))
24	24	1. Erkennst du eine Symmetrie?
25		-Die Funktion {{formula}} f(x) = \frac{1}{x} {{/formula}} ist punktsymmetrisch zur Ursprungsgeraden, da gilt:
26		-{{formula}}
27		-f(-x) = -f(x)
28		-{{/formula}}
29		-Das bedeutet, dass die Funktion eine Symmetrie bezüglich des Ursprungs hat.
30		-
31	31	1. Beschreibe das Randverhalten der Funktion und nenne ihre Wertemenge.
32	32	1. Bestimme {{formula}}g(y){{/formula}} für {{formula}}y=g(x){{/formula}} und {{formula}}x\in \mathbb{R}^*{{/formula}}.