Question

construa o gráfico das funções e verifique se é crescente ou decrescente: f(x)=-x+1​

Answer 1

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

$\large\boxed{\begin{array}{l}\underline{\rm Gr\acute afico}\\\sf \acute e~uma~reta~inclinada~e~pode~ser~obtida\\\sf a~partir~de~dois~pontos:\\\sf\bigodot 1~o~ponto~que~corta~o~eixo~x~(basta~fazer~y=0)\\\sf e~o~ponto~ser\acute a~da~forma~A(x,0)\\\sf\bigodot 2~o~ponto~que~reta~corta~o~eixo~y~(basta~fazer~x=0)\\\sf e~o~ponto~ser\acute a~da~forma~B(0,y)\end{array}}$

$\Large\boxed{\begin{array}{l}\sf f(x)=-x+1\\\sf como~a=-1<0~o~gr\acute afico~\acute e~decrescente.\\\underline{\rm intersecc_{\!\!,}\tilde ao~da~reta~com~o~eixo~x:}\\\sf f(x)=y=0\\\sf -x+1=0\\\sf x=1\\\sf A(1,0).\\\underline{\rm intersecc_{\!\!,}\tilde ao~da~reta~com~eixo~y:}\\\sf x=0\\\sf f(0)=0+1=1\\\sf B(0,1)\\\tt o~gr\acute afico~est\acute a~anexo\end{array}}$