Wiki-Quellcode von Lösung Eigenschaften
Version 15.1 von Holger Engels am 2023/11/10 11:07
Verstecke letzte Bearbeiter
| author | version | line-number | content |
|---|---|---|---|
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3.1 | 1 | a) |
| 2 | {{formula}}f(x)=\frac{1}{2}(x+2)^4+3{{/formula}} | ||
| 3 | (1) Globaler Verlauf: | ||
| 4 | Für {{formula}}x\rightarrow + \infty{{/formula}} gilt: {{formula}}f(x)\rightarrow + \infty{{/formula}} | ||
| 5 | Für {{formula}}x\rightarrow - \infty{{/formula}} gilt: {{formula}}f(x)\rightarrow + \infty{{/formula}} | ||
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5.1 | 6 | |
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3.1 | 7 | (2) Symmetrie: |
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4.1 | 8 | Achsensymmetrie zu {{formula}}x=-2{{/formula}} |
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1.1 | 9 | |
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5.1 | 10 | (3) Definitionsmenge: |
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6.1 | 11 | {{formula}}D_f=\mathbb R{{/formula}} |
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5.1 | 12 | |
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6.2 | 13 | (4) Wertemenge: |
| 14 | {{formula}}W_f=\{x\in\mathbb R|x\geq 3\}{{/formula}} | ||
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7.1 | 15 | |
| 16 | (5) keine Asymptote | ||
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8.1 | 17 | |
| 18 | |||
| 19 | b) | ||
| 20 | |||
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15.1 | 21 | [[image:geogebra-export.png||style="float: right" width="400"]] |
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10.1 | 22 | |
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12.1 | 23 | (1) Globaler Verlauf: |
| 24 | Für {{formula}}x\rightarrow + \infty{{/formula}} gilt: {{formula}}f(x)\rightarrow + 4{{/formula}} | ||
| 25 | Für {{formula}}x\rightarrow - \infty{{/formula}} gilt: {{formula}}f(x)\rightarrow + 4{{/formula}} | ||
| 26 | |||
| 27 | (2) Keine Symmetrie zu Achsen oder Ursprung | ||
| 28 | |||
| 29 | (3) Definitionsmenge: | ||
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12.2 | 30 | {{formula}}D_h=\mathbb R\backslash\{2\}\{{/formula}} |
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12.1 | 31 | |
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13.1 | 32 | (4) Wertemenge: |
| 33 | {{formula}}W_h=\mathbb R\backslash\{4\}\{{/formula}} | ||
| 34 | |||
| 35 | (5) Asymptoten: | ||
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14.1 | 36 | Senkrechte Asymptote: {{formula}}x=2{{/formula}} |
| 37 | Waagrechte Asymptote: {{formula}}y=4{{/formula}} | ||
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13.1 | 38 | |
| 39 | |||
| 40 |