Wiki-Quellcode von Lösung Symmetrie untersuchen
Zuletzt geändert von Niklas Wunder am 2024/10/27 09:49
Verstecke letzte Bearbeiter
| author | version | line-number | content |
|---|---|---|---|
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3.1 | 1 | Für Achsensymmetrie zur y-Achse gilt: {{formula}}f(x)=f(-x){{/formula}} |
| 2 | Für Punktsymmetrie zum Ursprung gilt: {{formula}}f(x)=-f(-x){{/formula}} | ||
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2.1 | 3 | |
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1.1 | 4 | (% class="noborder" %) |
| 5 | |(% colspan="2" %)((( | ||
| 6 | (% style="list-style:alphastyle" %) | ||
| 7 | 1. {{formula}}f(x)=3x+1{{/formula}}))) | ||
| |
2.1 | 8 | | (((Check y-Achse: {{formula}}f(-x)=3(-x)+1{{/formula}} |
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1.1 | 9 | {{formula}}\Rightarrow 3x+1\neq-3x+1{{/formula}} ↯ |
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2.1 | 10 | ))) | (((Check Ursprung: {{formula}}-f(-x)=-(3(-x)+1){{/formula}} |
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1.1 | 11 | {{formula}}\Rightarrow 3x+1\neq3x-1{{/formula}} ↯ |
| 12 | ))) | ||
| 13 | |(% colspan="2" %)((( | ||
| 14 | (% style="list-style:alphastyle" start="2" %) | ||
| 15 | 1. {{formula}}f(x)=7{{/formula}}))) | ||
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2.1 | 16 | | (((Check y-Achse: {{formula}}f(-x)=7{{/formula}} ✓ |
| 17 | ))) | (((Check Ursprung: {{formula}}-f(-x)=-7{{/formula}} ↯ | ||
| |
1.1 | 18 | ))) |
| 19 | |(% colspan="2" %)((( | ||
| 20 | (% style="list-style:alphastyle" start="3" %) | ||
| 21 | 1. {{formula}}f(x)=4x^3-8x+2{{/formula}}))) | ||
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4.1 | 22 | | (((Check y-Achse: {{formula}}f(-x)=4(-x)^3-8(-x)+2{{/formula}} |
| 23 | {{formula}}\Rightarrow 4x^3-8x+2\neq-4x^3+8x+2{{/formula}} ↯ | ||
| 24 | ))) | (((Check Ursprung: {{formula}}-f(-x)=-(4(-x)^3-8(-x)+2){{/formula}} | ||
| 25 | {{formula}}\Rightarrow 4x^3-8x+2\neq 4x^3-8x-2{{/formula}} ↯ | ||
| |
1.1 | 26 | ))) |
| 27 | |(% colspan="2" %)((( | ||
| 28 | (% style="list-style:alphastyle" start="4" %) | ||
| 29 | 1. {{formula}}f(x)=-2x^4-9x^2+3{{/formula}}))) | ||
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2.1 | 30 | | (((Check y-Achse: {{formula}}f(-x)=-2(-x)^4-9(-x)^2+3{{/formula}} |
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1.1 | 31 | {{formula}}\Rightarrow -2x^4-9x^2+3=-2x^4-9x^2+3{{/formula}} ✓ |
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2.1 | 32 | ))) | (((Check Ursprung: {{formula}}-f(-x)=-(-2(-x)^4-9(-x)^2+3){{/formula}} |
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1.1 | 33 | {{formula}}\Rightarrow -2x^4-9x^2+3 \neq 2x^4+9x^2-3{{/formula}} ↯ |
| 34 | ))) | ||
| 35 | |(% colspan="2" %)((( | ||
| 36 | (% style="list-style:alphastyle" start="5" %) | ||
| 37 | 1. {{formula}}f(x)=(x^2-2)^3{{/formula}}))) | ||
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2.1 | 38 | | (((Check y-Achse: {{formula}}f(-x)=((-x)^2-2)^3{{/formula}} |
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1.1 | 39 | {{formula}}\Rightarrow (x^2-2)^3=(x^2-2)^3{{/formula}} ✓ |
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2.1 | 40 | ))) | (((Check Ursprung: {{formula}}-f(-x)=-(((-x)^2-2)^3){{/formula}} |
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1.1 | 41 | {{formula}}\Rightarrow (x^2-2)^3\neq-(x^2-2)^3{{/formula}} ↯ |
| 42 | ))) | ||
| 43 | |(% colspan="2" %)((( | ||
| 44 | (% style="list-style:alphastyle" start="6" %) | ||
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5.1 | 45 | 1. {{formula}}f(x)=x^4(x^3-3)\cdot (1-x)=(x^7-3x^4)\cdot (1-x)=-x^8+x^7+3 x^5-3 x^4{{/formula}}))) |
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2.1 | 46 | | (((Check y-Achse: {{formula}}f(-x)=(-x)^4((-x)^3-3)\cdot (1-(-x)){{/formula}} |
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1.1 | 47 | {{formula}}\Rightarrow -x^8 + x^7 + 3 x^5 - 3 x^4=-x^8 - x^7 - 3 x^5 - 3 x^4{{/formula}} ↯ |
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2.1 | 48 | ))) | (((Check Ursprung: {{formula}}-f(-x)=-((-x)^4((-x)^3-3)\cdot (1-(-x))){{/formula}} |
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1.1 | 49 | {{formula}}\Rightarrow -x^8 + x^7 + 3 x^5 - 3 x^4 = x^8 + x^7 + 3 x^5 + 3 x^4{{/formula}} ↯ |
| 50 | ))) | ||
| 51 |