Question

Se y = -1 + 3.cos(x), então y varia no intervalo
a) [2, 4]
b) [-1, 1]
c) [-1, 3]
d) [-3, 1]
e) [-4, 2]

Answer 1

$\mathrm{y=-1+3\cos{x}\ \ \|\ \ \cos{x}\in[-1,1]}\\\\ \mathbf{*\ Valor\ m\'inimo\ (\cos{x}=-1):}}\\\\ \mathrm{y=-1+3.(-1)=-1-3=-4\ \to\ y\limits_{m\'in}}=-4}\\\\ \mathbf{*\ Valor\ m\'aximo\ (\cos{x}=1):}\\\\ \mathrm{y=-1+3.1=-1+3=2\ \to\ y\limits_{m\'ax}=2}\\\\ \mathbf{*\ Intervalo\ onde\ o\ valor\ de\ y\ varia:}\\\\ \mathrm{y\in[y_{m\'in}},y_{m\'ax}]\ \to\ e)\ \boxed{\mathbf{y\in[-4,2]}}}$