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O gráfico completo de uma função \(f\) é dado na figura abaixo: ![[Picture]](/rendered/understandingFunctions/exercises/piecewise2-b07b25bd665d036c7e28e2fb4485a3f6.svg)
Determine o domínio de \(f\). \[ \left [\class{xm-answer}{\cssId{xm-answer-1}{\phantom{\rule{7em}{1.5em}}}},\class{xm-answer}{\cssId{xm-answer-2}{\phantom{\rule{7em}{1.5em}}}}\right ] \]
Determine a imagem de \(f\). \[ \left [\class{xm-answer}{\cssId{xm-answer-3}{\phantom{\rule{7em}{1.5em}}}},\class{xm-answer}{\cssId{xm-answer-4}{\phantom{\rule{7em}{1.5em}}}}\right ) \cup \left [\class{xm-answer}{\cssId{xm-answer-5}{\phantom{\rule{7em}{1.5em}}}},\class{xm-answer}{\cssId{xm-answer-6}{\phantom{\rule{7em}{1.5em}}}}\right ) \]
Encontre uma expressão para \(f(x)\) se \(0<x<2\). \[ f(x) = \class{xm-answer}{\cssId{xm-answer-7}{\phantom{\rule{7em}{1.5em}}}} \quad \text {para $0<x<2$.} \]
O gráfico de uma função \(g\) é dado abaixo. Ele foi obtido transladando e reescalando
o gráfico de \(f\). ![[Picture]](/rendered/understandingFunctions/exercises/piecewise2-9dba46e1c77eb12e593ee47a0b9612e9.svg)
Encontre a
expressão da função \(g\). \[ g(x) = \class{xm-answer}{\cssId{xm-answer-8}{\phantom{\rule{7em}{1.5em}}}} \cdot f\left (\class{xm-answer}{\cssId{xm-answer-9}{\phantom{\rule{7em}{1.5em}}}}\right ) \]
Determine o domínio de \(g\). \[ \left [\class{xm-answer}{\cssId{xm-answer-10}{\phantom{\rule{7em}{1.5em}}}},\class{xm-answer}{\cssId{xm-answer-11}{\phantom{\rule{7em}{1.5em}}}}\right ] \] Determine a imagem de \(g\). \[ \left (\class{xm-answer}{\cssId{xm-answer-12}{\phantom{\rule{7em}{1.5em}}}},\class{xm-answer}{\cssId{xm-answer-13}{\phantom{\rule{7em}{1.5em}}}}\right ] \cup \left (\class{xm-answer}{\cssId{xm-answer-14}{\phantom{\rule{7em}{1.5em}}}},\class{xm-answer}{\cssId{xm-answer-15}{\phantom{\rule{7em}{1.5em}}}}\right ] \]
Seja \(F\) uma função ímpar definida em \([-4,4]\) tal que \(F(x) = f(x)\) se \(0\le x\le 4\):
![[Picture]](/rendered/understandingFunctions/exercises/piecewise2-d9302281b297d605f9e5174286a47f0e.svg)
Encontre uma expressão para \(F(x)\)
se \(-4\le x\le 0\).
Sua resposta deve conter a letra \(f\).
xmhintLembre-se: \(F\) é ímpar!
\[ F(x) = \class{xm-answer}{\cssId{xm-answer-16}{\phantom{\rule{7em}{1.5em}}}} \quad \text {para $-4\le x<0$.} \] Isso significa que, para todo \(x\) no domínio de \(F\),
\(F(-x)=-F(x)\)