1) Dada a função f: [math]\mathbb{R}\longrightarrow\mathbb{R}[/math] definida por:[br][center][img width=89,height=19]data:image/png;base64,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[/img] [/center]Calcule:[br][br]a) f(–1)[br][br]b) f(1)[br][br]c) f(0)
a) f(–1) = (–1)² – 2[br]f(–1) = 1 – 2[br]f(–1) = –1[br][br]b) f(1) = 1² – 2[br]f(1) = 1 – 2[br]f(1) = – 1[br][br]c) f(0) = 0² – 2[br]f(0) = – 2
2) Calcule a raiz da função:[br] [center][img width=90,height=18]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHAAAAAXCAMAAADkzzubAAAAAXNSR0IArs4c6QAAAIFQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6Ojo6OjpmOjqQOmaQOma2OpC2OpDbZgAAZjoAZmaQZrbbZrb/kDoAkDpmkGY6kLaQkLbbkNv/tmYAtmY6tpA6tpBmttv/tv//25A625Bm27Zm27aQ2////7Zm/9uQ/9u2//+2///bA6B96AAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABm0lEQVRIS+2V2XaDIBCGIbHaLY1dbBJpm5BFI+//gIUZhqWiaXuOd+HCw1F+/plvBmTsOiYmoL4edoGFfNxOYnhecZ6bnVX1dIoc2ru3CRy7Mj/JJfiZZ+x4Ww87quMz59nIAi+FlYRLzi3GhiYh1Zs459Be8Fd2LhOiXoxytmFK2JVdZfdUFXD9fYrCrJf8MvWuNOjwqQV6gGVboFStuP7yMQNWCcxxRI0xjCSJqGFnZTMjH9agBdvXGvKe4oY0RgaAiiW91ZgbGZKPM2R6tl6QSljgwpCAYePCBRRuKOmHJ+Y1U58IkklqC9c8mnamw8ZBhukkHfFQwnrBaeQ8W5f27BEzl2pUuFFD32cXa21gQNPY3tEzb9gU/jBQDZNIRU6HJpQMVFxiLVzP+Fn3cnCHy8eT2Aaq0UDLB5IBP32/wBfrC12Eb9T7TkdxwDZtR64a+KaENowkacNjsUAaQY3wpjERqIrbNnUtldjGUl7+kKQM2+J+g+/D6+Wvd+kAu/HXvoTgPv3fgm5Um+/k/8PS/TP+xecq6hH4BovJIhdAZY3FAAAAAElFTkSuQmCC[/img][/center]
[i]x = –b/a[br]x = –(–9)/2[br]x = 9/2[br]x = 4,5[/i]
3) Dada as funções[br][br][center] [img width=90,height=18]data:image/png;base64,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[/img] e [img width=94,height=18]data:image/png;base64,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[/img][/center] Determine:[br][br]a) f(x + 1) [br][br]b) g(x – 2)
a) f(x) = 2x – 3[br]f(x + 1) = 2x – 3[br]f(x + 1) = 2 * (x + 1) – 3[br]f(x + 1) = 2x + 2 – 3[br]f(x + 1) = 2x – 1[br][br]b) g(x) = – x + 4[br]g(x – 2) = – (x – 2) +4[br]g(x – 2) = – x + 2 + 4[br]g(x – 2) = – x + 6[br]
4) Considere as afirmações sobre a função: [img width=64,height=18]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFAAAAAXCAMAAACrkjhLAAAAAXNSR0IArs4c6QAAAHhQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OjoAOjo6OjqQOmaQOma2OpC2OpDbZgAAZmaQZrb/kDoAkDpmkGY6kLaQkLbbkNv/tmYAtmY6tpBmttv/tv//25A625Bm27Zm27aQ2////7Zm/9uQ/9u2//+2///bB/Bi6QAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABT0lEQVRIS+VU21LDIBBl21iqthrFaFFLYwnw/38oLPc28ZK+OOM+ZDID5+zuObsQ8u/DvN3uCxHE5n2WJKoDWDmkYXfHimG4eZzBqNvVUdwjn/vWjOvdNKPprwGa8wtiGdqU8afs+qquuaTnixei2OKUUbOAMQz7/nmJ3N0XcKKKABtIOVB/ZDqwrb/6zCMy1Bm5a6uCRB4iQ/GHnRXhEPNiGZOhOhyEChJ5EiGxf8/byMGDINx1gpFF0y3AxmtcQESUPZlDdNukcYyEE0V+UO9khmQrUqmVcN8QEukEL7XWbRy+TChpHpao4VjLjmmgiM+Q5ElymeiHPk1kznfWsx8AiWNTQETSODZvnvY2S+9tHqZXxbiZVjjFJaTQyG+Ky2AYBJuTZSOmqI4CbC1fCSnX47e7PGp8lhCtuvy1wc1Jcfl72DbzntCv1vFvn30CriobAI8Ys88AAAAASUVORK5CYII=[/img][i][b][br][br]I[/b][/i]. O gráfico da função é uma reta.[br]II. Para cada valor de [i]x[/i], a respectiva imagem é o triplo.[br]III. O gráfico da função cruza o ponto (2,3).[br]Está correto o que se afirma em:
5) Seja, [img width=68,height=18]data:image/png;base64,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[/img].[br] Em relação às características de [i]g[/i], é correto afirmar que: