Question

O gráfico de f(x)=3.sen x é análogo ao de y=sen x, com a amplitude aumentando de 1 para 3 unidades, ou seja, os valores de f(x) oscilarão entre +3 e -3. Faça o esboço desse gráfico no plano a seguir.​

Answer 1

Explicação passo-a-passo:

$\sf f(x)=3\cdot sen~x$

• Para $\sf x=-2\pi~rad$:

$\sf f(-2\pi)=3\cdot sen~(-2\pi)$

$\sf f(-2\pi)=3\cdot(-1)\cdot sen~(2\pi)$

$\sf f(-2\pi)=3\cdot(-1)\cdot0$

$\sf f(-2\pi)=0$

• Para $\sf x=\dfrac{-3\pi}{2}~rad$:

$\sf f\Big(\dfrac{-3\pi}{2}\Big)=3\cdot sen~\Big(\dfrac{-3\pi}{2}\Big)$

$\sf f\Big(\dfrac{-3\pi}{2}\Big)=3\cdot(-1)\cdot sen~\Big(\dfrac{3\pi}{2}\Big)$

$\sf f\Big(\dfrac{-3\pi}{2}\Big)=3\cdot(-1)\cdot(-1)$

$\sf f\Big(\dfrac{-3\pi}{2}\Big)=3$

• Para $\sf x=-\pi~rad$:

$\sf f(-\pi)=3\cdot sen~(-\pi)$

$\sf f(-\pi)=3\cdot(-1)\cdot sen~(\pi)$

$\sf f(-\pi)=3\cdot(-1)\cdot0$

$\sf f(-\pi)=0$

• Para $\sf x=\dfrac{-\pi}{2}~rad$:

$\sf f\Big(\dfrac{-\pi}{2}\Big)=3\cdot sen~\Big(\dfrac{-\pi}{2}\Big)$

$\sf f\Big(\dfrac{-\pi}{2}\Big)=3\cdot(-1)\cdot sen~\Big(\dfrac{\pi}{2}\Big)$

$\sf f\Big(\dfrac{-\pi}{2}\Big)=3\cdot(-1)\cdot1$

$\sf f\Big(\dfrac{-\pi}{2}\Big)=-3$

• Para $\sf x=0$:

$\sf f(0)=3\cdot sen~0:$

$\sf f(0)=3\cdot0$

$\sf f(0)=0$

• Para $\sf x=\dfrac{\pi}{2}~rad$:

$\sf f\Big(\dfrac{\pi}{2}\Big)=3\cdot sen~\Big(\dfrac{\pi}{2}\Big)$

$\sf f\Big(\dfrac{\pi}{2}\Big)=3\cdot1$

$\sf f\Big(\dfrac{\pi}{2}\Big)=3$

• Para $\sf x=\pi~rad$:

$\sf f(\pi)=3\cdot sen~(\pi)$

$\sf f(\pi)=3\cdot0$

$\sf f(\pi)=0$

• Para $\sf x=\dfrac{3\pi}{2}~rad$:

$\sf f\Big(\dfrac{3\pi}{2}\Big)=3\cdot sen~\Big(\dfrac{3\pi}{2}\Big)$

$\sf f\Big(\dfrac{3\pi}{2}\Big)=3\cdot(-1)$

$\sf f\Big(\dfrac{3\pi}{2}\Big)=-3$

• Para $\sf x=2\pi~rad$:

$\sf f(2\pi)=3\cdot sen~(2\pi)$

$\sf f(2\pi)=3\cdot0$

$\sf f(2\pi)=0$