Question

Escreva uma função afim para cada item abaixo g(0)=-5 e g(2)=6 h(-4)=6 e h(0)=0 por favor me ajudem

Answer 1

A função afim (função de 1° grau) é dada na forma:  f(x) = a.x + b

a)

Vamos substituir os pontos dados.

$Utilizando~o~ponto~g(0)~=\,-5\\\\g(0)~=~a\,.\,(0)+b\\\\\\-5~=~0+b\\\\\\\boxed{b~=\,-5}\\\\\\\\Utilizando~o~ponto~g(2)~=\,6\\\\g(2)~=~a\,.\,(2)+(-5)\\\\\\6~=~2a-5\\\\\\2a~=~6+5\\\\\\\boxed{a~=~\frac{11}{2}}\\\\\\\\A~funcao~g(x)~fica:\\\\\boxed{g(x)~=~\frac{11}{2}x-5}$

b)

Vamos substituir os pontos dados.

$Utilizando~o~ponto~h(0)~=~0\\\\h(0)~=~a\,.\,(0)+b\\\\\\0~=~0+b\\\\\\\boxed{b~=~0}\\\\\\\\Utilizando~o~ponto~h(-4)~=~6\\\\h(-4)~=~a\,.\,(-4)+(0)\\\\\\6~=\,-4a\\\\\\a~=\,-\frac{6}{4}\\\\\\\boxed{a~=\,-\frac{3}{2}}\\\\\\\\A~funcao~h(x)~fica:\\\\\boxed{h(x)~=\,-\frac{3}{2}x}$