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Version 5.1 von Niklas Wunder am 2024/10/27 08:25
Zeige letzte Bearbeiter
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}}
3
4 (% class="noborder" %)
5 |(% colspan="2" %)(((
6 (% style="list-style:alphastyle" %)
7 1. {{formula}}f(x)=3x+1{{/formula}})))
8 | (((Check y-Achse: {{formula}}f(-x)=3(-x)+1{{/formula}}
9 {{formula}}\Rightarrow 3x+1\neq-3x+1{{/formula}} ↯
10 ))) | (((Check Ursprung: {{formula}}-f(-x)=-(3(-x)+1){{/formula}}
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}})))
16 | (((Check y-Achse: {{formula}}f(-x)=7{{/formula}} ✓
17 ))) | (((Check Ursprung: {{formula}}-f(-x)=-7{{/formula}} ↯
18 )))
19 |(% colspan="2" %)(((
20 (% style="list-style:alphastyle" start="3" %)
21 1. {{formula}}f(x)=4x^3-8x+2{{/formula}})))
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}} ↯
26 )))
27 |(% colspan="2" %)(((
28 (% style="list-style:alphastyle" start="4" %)
29 1. {{formula}}f(x)=-2x^4-9x^2+3{{/formula}})))
30 | (((Check y-Achse: {{formula}}f(-x)=-2(-x)^4-9(-x)^2+3{{/formula}}
31 {{formula}}\Rightarrow -2x^4-9x^2+3=-2x^4-9x^2+3{{/formula}} ✓
32 ))) | (((Check Ursprung: {{formula}}-f(-x)=-(-2(-x)^4-9(-x)^2+3){{/formula}}
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}})))
38 | (((Check y-Achse: {{formula}}f(-x)=((-x)^2-2)^3{{/formula}}
39 {{formula}}\Rightarrow (x^2-2)^3=(x^2-2)^3{{/formula}} ✓
40 ))) | (((Check Ursprung: {{formula}}-f(-x)=-(((-x)^2-2)^3){{/formula}}
41 {{formula}}\Rightarrow (x^2-2)^3\neq-(x^2-2)^3{{/formula}} ↯
42 )))
43 |(% colspan="2" %)(((
44 (% style="list-style:alphastyle" start="6" %)
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}})))
46 | (((Check y-Achse: {{formula}}f(-x)=(-x)^4((-x)^3-3)\cdot (1-(-x)){{/formula}}
47 {{formula}}\Rightarrow -x^8 + x^7 + 3 x^5 - 3 x^4=-x^8 - x^7 - 3 x^5 - 3 x^4{{/formula}} ↯
48 ))) | (((Check Ursprung: {{formula}}-f(-x)=-((-x)^4((-x)^3-3)\cdot (1-(-x))){{/formula}}
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 )))