Änderungen von Dokument Lösung Symmetrie untersuchen

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...	...	@@ -1,48 +1,51 @@
	1	+Für Symmetrie zur y-Achse gilt: {{formula}}f(x)=f(-x){{/formula}}
	2	+Für Symmetrie zum Ursprung gilt: {{formula}}f(x)=-f(-x){{/formula}}
	3	+
1	1	(% class="noborder" %)
2	2	|(% colspan="2" %)(((
3	3	(% style="list-style:alphastyle" %)
4	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}}
	8	+| (((Check y-Achse: {{formula}}f(-x)=3(-x)+1{{/formula}}
6	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}}
	10	+))) | (((Check Ursprung: {{formula}}-f(-x)=-(3(-x)+1){{/formula}}
8	8	{{formula}}\Rightarrow 3x+1\neq3x-1{{/formula}} ↯
9	9	)))
10	10	|(% colspan="2" %)(((
11	11	(% style="list-style:alphastyle" start="2" %)
12	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}} ↯
	16	+| (((Check y-Achse: {{formula}}f(-x)=7{{/formula}} ✓
	17	+))) | (((Check Ursprung: {{formula}}-f(-x)=-7{{/formula}} ↯
15	15	)))
16	16	|(% colspan="2" %)(((
17	17	(% style="list-style:alphastyle" start="3" %)
18	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}}
	22	+| (((Check y-Achse: {{formula}}f(-x)=3(-x)^3-8(-x)+2{{/formula}}
20	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}}
	24	+))) | (((Check Ursprung: {{formula}}-f(-x)=-(3(-x)^3-8(-x)+2){{/formula}}
22	22	{{formula}}\Rightarrow 3x^3-8x+2\neq3x^3-8x-2{{/formula}} ↯
23	23	)))
24	24	|(% colspan="2" %)(((
25	25	(% style="list-style:alphastyle" start="4" %)
26	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}}
	30	+| (((Check y-Achse: {{formula}}f(-x)=-2(-x)^4-9(-x)^2+3{{/formula}}
28	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}}
	32	+))) | (((Check Ursprung: {{formula}}-f(-x)=-(-2(-x)^4-9(-x)^2+3){{/formula}}
30	30	{{formula}}\Rightarrow -2x^4-9x^2+3 \neq 2x^4+9x^2-3{{/formula}} ↯
31	31	)))
32	32	|(% colspan="2" %)(((
33	33	(% style="list-style:alphastyle" start="5" %)
34	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}}
	38	+| (((Check y-Achse: {{formula}}f(-x)=((-x)^2-2)^3{{/formula}}
36	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}}
	40	+))) | (((Check Ursprung: {{formula}}-f(-x)=-(((-x)^2-2)^3){{/formula}}
38	38	{{formula}}\Rightarrow (x^2-2)^3\neq-(x^2-2)^3{{/formula}} ↯
39	39	)))
40	40	|(% colspan="2" %)(((
41	41	(% style="list-style:alphastyle" start="6" %)
42	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}}
	46	+| (((Check y-Achse: {{formula}}f(-x)=(-x)^4((-x)^3-3)\cdot (1-(-x)){{/formula}}
44	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}}
	48	+))) | (((Check Ursprung: {{formula}}-f(-x)=-((-x)^4((-x)^3-3)\cdot (1-(-x))){{/formula}}
46	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	47	)))
48	48