Änderungen von Dokument Lösung Symmetrie untersuchen

Zusammenfassung

• Seiteneigenschaften (1 geändert, 0 hinzugefügt, 0 gelöscht)

Details

Seiteneigenschaften

Inhalt

...	...	@@ -1,51 +4,48 @@
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		-
4	4	(% class="noborder" %)
5	5	|(% colspan="2" %)(((
6	6	(% style="list-style:alphastyle" %)
7	7	1. {{formula}}f(x)=3x+1{{/formula}})))
8		-| (((Check y-Achse: {{formula}}f(-x)=3(-x)+1{{/formula}}
	5	+| (((Check y-Achse: {{formula}}f(x)\overset{?}{=}f(-x)\Rightarrow 3x+1=3(-x)+1{{/formula}}
9	9	{{formula}}\Rightarrow 3x+1\neq-3x+1{{/formula}} ↯
10		-))) | (((Check Ursprung: {{formula}}-f(-x)=-(3(-x)+1){{/formula}}
	7	+))) | (((Check Ursprung: {{formula}}f(x)\overset{?}{=}-f(-x)\Rightarrow 3x+1=-(3(-x)+1){{/formula}}
11	11	{{formula}}\Rightarrow 3x+1\neq3x-1{{/formula}} ↯
12	12	)))
13	13	|(% colspan="2" %)(((
14	14	(% style="list-style:alphastyle" start="2" %)
15	15	1. {{formula}}f(x)=7{{/formula}})))
16		-| (((Check y-Achse: {{formula}}f(-x)=7{{/formula}} ✓
17		-))) | (((Check Ursprung: {{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}} ↯
18	18	)))
19	19	|(% colspan="2" %)(((
20	20	(% style="list-style:alphastyle" start="3" %)
21	21	1. {{formula}}f(x)=4x^3-8x+2{{/formula}})))
22		-| (((Check y-Achse: {{formula}}f(-x)=3(-x)^3-8(-x)+2{{/formula}}
	19	+| (((Check y-Achse: {{formula}}f(x)\overset{?}{=}f(-x)\Rightarrow 3x^3-8x+2=3(-x)^3-8(-x)+2{{/formula}}
23	23	{{formula}}\Rightarrow 3x^3-8x+2\neq-3x^3+8x+2{{/formula}} ↯
24		-))) | (((Check Ursprung: {{formula}}-f(-x)=-(3(-x)^3-8(-x)+2){{/formula}}
	21	+))) | (((Check Ursprung: {{formula}}f(x)\overset{?}{=}-f(-x)\Rightarrow 3x^3-8x+2=-(3(-x)^3-8(-x)+2){{/formula}}
25	25	{{formula}}\Rightarrow 3x^3-8x+2\neq3x^3-8x-2{{/formula}} ↯
26	26	)))
27	27	|(% colspan="2" %)(((
28	28	(% style="list-style:alphastyle" start="4" %)
29	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}}
	27	+| (((Check y-Achse: {{formula}}f(x)\overset{?}{=}f(-x)\Rightarrow -2x^4-9x^2+3=-2(-x)^4-9(-x)^2+3{{/formula}}
31	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}}
	29	+))) | (((Check Ursprung: {{formula}}f(x)\overset{?}{=}-f(-x)\Rightarrow -2x^4-9x^2+3=-(-2(-x)^4-9(-x)^2+3){{/formula}}
33	33	{{formula}}\Rightarrow -2x^4-9x^2+3 \neq 2x^4+9x^2-3{{/formula}} ↯
34	34	)))
35	35	|(% colspan="2" %)(((
36	36	(% style="list-style:alphastyle" start="5" %)
37	37	1. {{formula}}f(x)=(x^2-2)^3{{/formula}})))
38		-| (((Check y-Achse: {{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}}
39	39	{{formula}}\Rightarrow (x^2-2)^3=(x^2-2)^3{{/formula}} ✓
40		-))) | (((Check Ursprung: {{formula}}-f(-x)=-(((-x)^2-2)^3){{/formula}}
	37	+))) | (((Check Ursprung: {{formula}}f(x)\overset{?}{=}-f(-x)\Rightarrow (x^2-2)^3=-(((-x)^2-2)^3){{/formula}}
41	41	{{formula}}\Rightarrow (x^2-2)^3\neq-(x^2-2)^3{{/formula}} ↯
42	42	)))
43	43	|(% colspan="2" %)(((
44	44	(% style="list-style:alphastyle" start="6" %)
45	45	1. {{formula}}f(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}}
	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}}
47	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}}
	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}}
49	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	50	)))
51	51