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Version 1.1 von Holger Engels am 2024/10/25 21:06
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1 (% class="noborder" %)
2 |(% colspan="2" %)(((
3 (% style="list-style:alphastyle" %)
4 1. {{formula}}f(x)=3x+1{{/formula}})))
5 | (((Check y-Achse: {{formula}}f(x)\overset{?}{=}f(-x)\Rightarrow 3x+1=3(-x)+1{{/formula}}
6 {{formula}}\Rightarrow 3x+1\neq-3x+1{{/formula}} ↯
7 ))) | (((Check Ursprung: {{formula}}f(x)\overset{?}{=}-f(-x)\Rightarrow 3x+1=-(3(-x)+1){{/formula}}
8 {{formula}}\Rightarrow 3x+1\neq3x-1{{/formula}} ↯
9 )))
10 |(% colspan="2" %)(((
11 (% style="list-style:alphastyle" start="2" %)
12 1. {{formula}}f(x)=7{{/formula}})))
13 | (((Check y-Achse: {{formula}}f(x)\overset{?}{=}f(-x)\Rightarrow 7=7{{/formula}} ✓
14 ))) | (((Check Ursprung: {{formula}}f(x)\overset{?}{=}-f(-x)\Rightarrow 7=-7{{/formula}} ↯
15 )))
16 |(% colspan="2" %)(((
17 (% style="list-style:alphastyle" start="3" %)
18 1. {{formula}}f(x)=4x^3-8x+2{{/formula}})))
19 | (((Check y-Achse: {{formula}}f(x)\overset{?}{=}f(-x)\Rightarrow 3x^3-8x+2=3(-x)^3-8(-x)+2{{/formula}}
20 {{formula}}\Rightarrow 3x^3-8x+2\neq-3x^3+8x+2{{/formula}} ↯
21 ))) | (((Check Ursprung: {{formula}}f(x)\overset{?}{=}-f(-x)\Rightarrow 3x^3-8x+2=-(3(-x)^3-8(-x)+2){{/formula}}
22 {{formula}}\Rightarrow 3x^3-8x+2\neq3x^3-8x-2{{/formula}} ↯
23 )))
24 |(% colspan="2" %)(((
25 (% style="list-style:alphastyle" start="4" %)
26 1. {{formula}}f(x)=-2x^4-9x^2+3{{/formula}})))
27 | (((Check y-Achse: {{formula}}f(x)\overset{?}{=}f(-x)\Rightarrow -2x^4-9x^2+3=-2(-x)^4-9(-x)^2+3{{/formula}}
28 {{formula}}\Rightarrow -2x^4-9x^2+3=-2x^4-9x^2+3{{/formula}} ✓
29 ))) | (((Check Ursprung: {{formula}}f(x)\overset{?}{=}-f(-x)\Rightarrow -2x^4-9x^2+3=-(-2(-x)^4-9(-x)^2+3){{/formula}}
30 {{formula}}\Rightarrow -2x^4-9x^2+3 \neq 2x^4+9x^2-3{{/formula}} ↯
31 )))
32 |(% colspan="2" %)(((
33 (% style="list-style:alphastyle" start="5" %)
34 1. {{formula}}f(x)=(x^2-2)^3{{/formula}})))
35 | (((Check y-Achse: {{formula}}f(x)\overset{?}{=}f(-x)\Rightarrow (x^2-2)^3=((-x)^2-2)^3{{/formula}}
36 {{formula}}\Rightarrow (x^2-2)^3=(x^2-2)^3{{/formula}} ✓
37 ))) | (((Check Ursprung: {{formula}}f(x)\overset{?}{=}-f(-x)\Rightarrow (x^2-2)^3=-(((-x)^2-2)^3){{/formula}}
38 {{formula}}\Rightarrow (x^2-2)^3\neq-(x^2-2)^3{{/formula}} ↯
39 )))
40 |(% colspan="2" %)(((
41 (% style="list-style:alphastyle" start="6" %)
42 1. {{formula}}f(x)=x^4(x^3-3)\cdot (1-x){{/formula}})))
43 | (((Check y-Achse: {{formula}}f(x)\overset{?}{=}f(-x)\Rightarrow x^4(x^3-3)\cdot (1-x)=(-x)^4((-x)^3-3)\cdot (1-(-x)){{/formula}}
44 {{formula}}\Rightarrow -x^8 + x^7 + 3 x^5 - 3 x^4=-x^8 - x^7 - 3 x^5 - 3 x^4{{/formula}} ↯
45 ))) | (((Check Ursprung: {{formula}}f(x)\overset{?}{=}-f(-x)\Rightarrow x^4(x^3-3)\cdot (1-x)=-((-x)^4((-x)^3-3)\cdot (1-(-x))){{/formula}}
46 {{formula}}\Rightarrow -x^8 + x^7 + 3 x^5 - 3 x^4 = x^8 + x^7 + 3 x^5 + 3 x^4{{/formula}} ↯
47 )))