Question

Estude o sinal da função do 1o grau:
a) y = 3x+9
b) y = -4x+16
c) y= 6x-30
d) y= -2x+1

Answer 1

a)

$\mathtt{f(x)=3x+9}$

$\mathtt{a=3>0\to~crescente}$

raiz:

$\mathtt{x=-\dfrac{9}{3}=-3}$

$\mathtt{f(x)>0\to, x>-3}\\\mathtt{f(x) \textless0\to~x<-3}$

b)

$\mathtt{g(x)=-4x+16}$

$\mathtt{a=-4\textless~0\to~decrescente}$

raiz:

$\mathtt{x=\dfrac{-16}{-4}=4}$

$\mathtt{g(x)>0\to, x\textless~4}\\\mathtt{g(x) \textless0\to~x>4}$

c)

$\mathtt{h(x)=6x-30}$

$\mathtt{a=6>~0\to~crescente}$

raiz:

$\mathtt{x=-\dfrac{-30}{6}=5}$

$\mathtt{h(x)>0\to, x>~5}\\\mathtt{h(x) \textless0\to~x\textless~5}$

d)

$\mathtt{p(x)=-2x+1}$

raiz:

$\mathtt{x=-\dfrac{1}{-2}=\dfrac{1}{2}}$

$\mathtt{p(x)>0\to, x\textless~\dfrac{1}{2}}\\\mathtt{p(x) \textless0\to~x>\dfrac{1}{2}}$