Question

Realize o estudo do sinal da função representada em cada gráfico.

Answer 1

$\Large\boxed{\begin{array}{l}\tt a)~\sf A(0,5)~~B(2,6)\\\sf m=\dfrac{6-5}{2-0}=\dfrac{1}{2}\\\sf y=5+\dfrac{1}{2}x\\\sf ra\acute iz:\\\sf x=-\dfrac{5}{\frac{1}{2}}=-5\cdot2=-10\\\sf f(x)>0~para~x>-10\\\sf f(x)<0~para~x<-10\end{array}}$

$\Large\boxed{\begin{array}{l}\tt b)~\sf f(x)>0\,\forall\,x\in\mathbb{R}\end{array}}$

$\Large\boxed{\begin{array}{l}\tt c)~\sf A(0,4)~B(3,-2)\\\sf m=\dfrac{-2-4}{3-0}=\dfrac{-6}{3}=-2\\\\\sf y=4-2\cdot(x-0)\\\sf y=4-2x\\\sf ra\acute iz:\\\sf x=\dfrac{-4}{-2}=2\\\sf f(x)>0~para~x>2\\\sf f(x)<0~para~x<2\end{array}}$