Question

55 pontos

Dadas as funções abaixo determine o coeficiente angular e coeficiente linear:
f(x) = -6x+15

f(x) = x-1

f(x) = 2x +3

f(x) = -x+5

Classifique em crescente e decrescente:
f(x) = x-20

f(x) = -2x

f(x) = -8x +3

f(x) = 3x-5

Answer 1

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$\Large\boxed{\underline{\sf Func_{\!\!,}\tilde ao~de~1^{\underline o}~grau}}\\\boxed{\begin{array}{c}\sf f(x)=ax+b,~com~a,b\in\mathbb{R},a\ne0\\\sf a\longrightarrow coeficiente~~angular\\\sf b\longrightarrow coeficiente~linear\\\sf se~a>0\implies func_{\!\!,}\tilde ao~crescente\\\sf se~a<0\implies func_{\!\!,}\tilde ao~decrescente\end{array}}$

$\rm 1)\\\tt a)~\sf f(x)=-6x+15\\\sf coeficiente~angular:-6~~coeficiente~linear:15\\\tt b)~\sf f(x)=x-1\\\sf coeficiente~angular:1~~coeficiente~linear:-1\\\tt c)~\sf f(x)=2x+3\\\sf coeficiente~angular:2~~coeficiente~linear:3\\\tt d)~\sf f(x)=-x+5\\\sf coeficiente~angular:-1~~coeficiente~linear:5$

$\rm 2)\\\tt a)~\sf f(x)=x-20\\\sf a=1>0\implies crescente\\\tt b)~\sf f(x)=-2x\\\sf a=-2><0\implies decrescente\\\tt c)~\sf-8x+3\\\sf a=-8<0\implies decrescente\\\tt d)~\sf f(x)=3x-5\\\sf a=3>0\implies crescente$