Wiki-Quellcode von Lösung Eigenschaften
Zuletzt geändert von Holger Engels am 2023/11/20 14:21
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| author | version | line-number | content |
|---|---|---|---|
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17.1 | 1 | a) [[image:Parabel 4. Ordnung.svg||style="float: right" width="300"]] {{formula}}f(x)=\frac{1}{2}(x+2)^4+3{{/formula}} |
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3.1 | 2 | (1) Globaler Verlauf: |
| 3 | Für {{formula}}x\rightarrow + \infty{{/formula}} gilt: {{formula}}f(x)\rightarrow + \infty{{/formula}} | ||
| 4 | Für {{formula}}x\rightarrow - \infty{{/formula}} gilt: {{formula}}f(x)\rightarrow + \infty{{/formula}} | ||
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5.1 | 5 | |
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3.1 | 6 | (2) Symmetrie: |
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4.1 | 7 | Achsensymmetrie zu {{formula}}x=-2{{/formula}} |
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1.1 | 8 | |
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5.1 | 9 | (3) Definitionsmenge: |
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6.1 | 10 | {{formula}}D_f=\mathbb R{{/formula}} |
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5.1 | 11 | |
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6.2 | 12 | (4) Wertemenge: |
| 13 | {{formula}}W_f=\{x\in\mathbb R|x\geq 3\}{{/formula}} | ||
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7.1 | 14 | |
| 15 | (5) keine Asymptote | ||
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8.1 | 16 | |
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17.1 | 17 | (% style="clear: right" %) |
| 18 | b) [[image:geogebra-export.png||style="float: right" width="400"]] | ||
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12.1 | 19 | (1) Globaler Verlauf: |
| 20 | Für {{formula}}x\rightarrow + \infty{{/formula}} gilt: {{formula}}f(x)\rightarrow + 4{{/formula}} | ||
| 21 | Für {{formula}}x\rightarrow - \infty{{/formula}} gilt: {{formula}}f(x)\rightarrow + 4{{/formula}} | ||
| 22 | |||
| 23 | (2) Keine Symmetrie zu Achsen oder Ursprung | ||
| 24 | |||
| 25 | (3) Definitionsmenge: | ||
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12.2 | 26 | {{formula}}D_h=\mathbb R\backslash\{2\}\{{/formula}} |
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12.1 | 27 | |
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13.1 | 28 | (4) Wertemenge: |
| 29 | {{formula}}W_h=\mathbb R\backslash\{4\}\{{/formula}} | ||
| 30 | |||
| 31 | (5) Asymptoten: | ||
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14.1 | 32 | Senkrechte Asymptote: {{formula}}x=2{{/formula}} |
| 33 | Waagrechte Asymptote: {{formula}}y=4{{/formula}} | ||
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13.1 | 34 | |
| 35 | |||
| 36 |