Introdu\303\247\303\243o \303\240s Fun\303\247\303\265es: Fun\303\247\303\265es Pares e \303\215mpares O Emaranhamento Qu\303\242ntico \303\251 peculiar, mas uma lei f\303\255sica bem estabelecida de part\303\255culas elementares. No seu mais b\303\241sico, afirma que duas part\303\255culas criadas de maneira particular, podem ser ligados de modo que h\303\241 uma correla\303\247\303\243o entre as propriedades de uma part\303\255cula e propriedades da outra part\303\255cula, independentemente do qu\303\243o distante as part\303\255culas est\303\243o. Essa correla\303\247\303\243o pode variar de -100% (anti-correlacionado) para 100% (correlacionado). At\303\251 mesmo Albert Einstein pensou nesta id\303\251ia que era estranha, chamando-o de "fantasmag\303\263rica a\303\247\303\243o \303\240 dist\303\242ncia".

JSFH Nesta apresenta\303\247\303\243o, vamos definir os termos fun\303\247\303\243o par e fun\303\247\303\243o \303\255mpar. Vamos supor que voc\303\252 esteja familiarizado com estes termos adicionais, que s\303\243o definidos em outras apresenta\303\247\303\265es desta cole\303\247\303\243o: gr\303\241fico, fun\303\247\303\243o, dom\303\255nio, sim\303\251trico em rela\303\247\303\243o ao eixo y, sim\303\251trico em rela\303\247\303\243o \303\240 origem, polinomiais e fun\303\247\303\243o de valor absoluto.

Se voc\303\252 pode reconhecer de alguma forma de simetria em tudo o que voc\303\252 est\303\241 estudando, voc\303\252 pode reduzir a quantidade de trabalho que voc\303\252 precisa fazer e tamb\303\251m reduzir as chances de certos tipos de erros. Nesta apresenta\303\247\303\243o, iremos analisar dois tipos de simetria matem\303\241tica, ou seja, fun\303\247\303\265es pares e \303\255mpares. Como eles se relacionam com as fun\303\247\303\265es, os termos pares e \303\255mpares v\303\252m das propriedades dos expoentes. Considere a fun\303\247\303\243o 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. Desde que o quadrado de um n\303\272mero negativo d\303\241 o mesmo resultado que o quadrado do n\303\272mero positivo correspondente, temos 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. Isso significa que o gr\303\241fico deLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LlEifkYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRS1JJW1zdXBHRiQ2JS1JI21pR0YkNiZRInhGJy8lJ2l0YWxpY0dRJXRydWVGJ0YvL0YzUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JVEiMkYnRi9GMkYvRjIvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRi9GMg== parece o mesmo para a esquerda e direita do eixo-y. Mais geralmente, se n \303\251 um algum n\303\272mero par (positivo ou negativo), ent\303\243o 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. Em seguida, considere a fun\303\247\303\243o 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. O valor de LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JlEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn em um n\303\272mero negativo est\303\241 tamb\303\251m relacionado com o valor de LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JlEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn no n\303\272mero positivo correspondente, mas de uma maneira diferente. Especificamente, 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. Isso significa que o gr\303\241fico de LUklbXN1cEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUklbXJvd0dGJDYlLUkjbW5HRiQ2JVEiM0YnRjIvRjZRJ25vcm1hbEYnRjJGPy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRic= \303\240 esquerda do eixo y tem a mesma apar\303\252ncia do gr\303\241fico \303\240 direita do eixo y, apenas de cabe\303\247a para baixo. Novamente, mais geralmente, se LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn \303\251 algum n\303\272mero \303\255mpar (positivos ou negativos), ent\303\243o, 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.

Fun\303\247\303\243o Par Uma fun\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYmUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGNy9GO1Enbm9ybWFsRidGK0Y3Rj0= \303\251 par se para qualquer LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn no dom\303\255nio de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn, temos 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. Note que isto significa o dom\303\255nio de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn deve ser sim\303\251trico cerca de 0, desde que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LlEqJnVtaW51czA7RicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZFLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnRi8vRjNRJ2l0YWxpY0YnRi9GMg== deve estar no dom\303\255nio, sempre que for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn. Qualquer fun\303\247\303\243o polinomial que s\303\263 tem termos com expoentes pares \303\251 uma fun\303\247\303\243o par. Outra fun\303\247\303\243o par muito importante \303\251 a fun\303\247\303\243o valor absoluto. Usando estes como blocos de constru\303\247\303\243o, voc\303\252 pode criar muitas fun\303\247\303\265es pares diferentes. O gr\303\241fico aqui \303\251 a fun\303\247\303\243o 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. 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alicGQ&false6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'normal6"-%-TRANSPARENCYG6#$""!!""-%*THICKNESSG6#""#-%%FONTG6$%&TIMESG"#7-%)_VISIBLEG6#"""-%%ROOTG6'-%)BOUNDS_XG6#$"$S"!""-%)BOUNDS_YG6#$"$I$!""-%-BOUNDS_WIDTHG6#$"%IP!""-%.BOUNDS_HEIGHTG6#$"%qN!""-%)CHILDRENG6"-%+ANNOTATIONG6'-%)BOUNDS_XG6#$"$S"!""-%)BOUNDS_YG6#$"$g#!""-%-BOUNDS_WIDTHG6#$"%gP!""-%.BOUNDS_HEIGHTG6#$"%qO!""-%)CHILDRENG6"Ig== Note que o gr\303\241fico de uma fun\303\247\303\243o par \303\251 sim\303\251trica em rela\303\247\303\243o \303\240 vertical do eixo (y).

Fun\303\247\303\243o \303\215mpar Uma fun\303\247\303\243o LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn \303\251 \303\255mpar se para qualquer LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn no dom\303\255nio de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn, temos 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. Note que isto significa que o dom\303\255nio de LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn deve ser sim\303\251trico cerca de 0, desde que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LlEqJnVtaW51czA7RicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZFLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnRi8vRjNRJ2l0YWxpY0YnRi9GMg== deve estar no dom\303\255nio sempre que for LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn. Qualquer fun\303\247\303\243o polinomial que s\303\263 tem termos com expoentes \303\255mpares \303\251 uma fun\303\247\303\243o \303\255mpar. A fun\303\247\303\243o rec\303\255proca, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiVRIjFGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnRjIvRjZRJ2l0YWxpY0YnRjJGNS8lLmxpbmV0aGlja25lc3NHRjEvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGRy8lKWJldmVsbGVkR0Y0RjJGNQ==, tamb\303\251m \303\251 uma fun\303\247\303\243o \303\255mpar. Usando estes como blocos de constru\303\247\303\243o, voc\303\252 pode criar muitas fun\303\247\303\265es \303\255mpares diferentes. O gr\303\241fico aqui \303\251 a fun\303\247\303\243o 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Note que o gr\303\241fico de uma fun\303\247\303\243o \303\255mpar \303\251 sim\303\251trico em rela\303\247\303\243o \303\240 origem.

A soma, diferen\303\247a, produto ou quociente de fun\303\247\303\265es pares \303\251 par. A soma ou diferen\303\247a de fun\303\247\303\265es \303\255mpares \303\251 \303\255mpar. No entanto, o produto ou quociente de fun\303\247\303\265es \303\255mpares \303\251 par, enquanto o produto ou quociente de uma fun\303\247\303\243o par e uma fun\303\247\303\243o \303\255mpar \303\251 \303\255mpar. Estas regras b\303\241sicas de aritm\303\251tica de fun\303\247\303\265es pares e \303\255mpares s\303\243o muito \303\272teis em ambas constru\303\247\303\243o de tais fun\303\247\303\265es e na an\303\241lise de outras fun\303\247\303\265es para determinar se elas t\303\252m essas importantes propriedades de simetria.

Desenhe a parte de uma fun\303\247\303\243o, quer \303\240 esquerda ou \303\240 direita do eixo-y. A outra metade do gr\303\241fico \303\251 desenhado para criar uma fun\303\247\303\243o par ou uma fun\303\247\303\243o \303\255mpar. Limpar um gr\303\241fico existente clicando sobre ela. M4_1_4b:-DrawEnd(); M4_1_4b:-DrawClick(); M4_1_4b:-DrawDrag(); 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NiI=M4_1_4b:-DoPlot();M4_1_4b:-DoPlot();

Duas part\303\255culas com correla\303\247\303\243o de 100% pode ser considerado como a defini\303\247\303\243o de uma fun\303\247\303\243o par. Quando um valor para um \303\251 medido em um determinado ponto, o outro ter\303\241 o mesmo valor, que \303\251 como avaliar uma fun\303\247\303\243o em uma determinada dist\303\242ncia da origem (positivos e negativos). Similarmente, duas part\303\255culas com correla\303\247\303\243o de 100% pode ser considerado como a defini\303\247\303\243o de uma fun\303\247\303\243o \303\255mpar. Explorar o conceito de correla\303\247\303\243o usando este exemplo interativo. Ajuste o controle deslizante para definir a correla\303\247\303\243o percentual desejada. Clicando e arrastando na janela do gr\303\241fico abaixo voc\303\252 pode desenhar o gr\303\241fico de uma fun\303\247\303\243o com a quantidade especificada de correla\303\247\303\243o. Limpar um gr\303\241fico existente clicando sobre ela. O que voc\303\252 percebe sobre a correla\303\247\303\243o completa? E quanto a n\303\243o haver correla\303\247\303\243o? M4_1_4a:-enddrag(); M4_1_4a:-click();M4_1_4a:-drag();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NiI=

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