Question

1) Construa o gráfico da função y= x – 3.​

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\rm Func_{\!\!,}\tilde ao~de~1^o~grau}\\\sf Chama-se~func_{\!\!,}\tilde ao~de~1^o~grau\\\sf a~toda~func_{\!\!,}\tilde ao~que~que~assume~a~forma\\\sf f(x)=ax+b~ou~y=ax+b\\\sf onde~a,b\in\mathbb{R}~e~a\ne0\\\end{array}}$

$\Large\boxed{\begin{array}{l}\underline{\rm caracter\acute isticas:}\\\sf\boxed{\sf1}~o~termo~a~\acute e~chamado~coeficiente~angular\\\sf e~o~termo~b~coeficiente~linear.\\\sf\boxed{2}~se~a>0~a~func_{\!\!,}\tilde ao~\acute e~crescente~\\\sf e~se~a<0~a~func_{\!\!,}\tilde ao~\acute e~decrescente\\\sf\boxed{\rm 3}~o~gr\acute afico~\acute e~uma~reta~inclinada\end{array}}$

$\rm Construc_{\!\!,}\tilde ao~do~gr\acute afico\\\sf para~construir~o~gr\acute afico~da~func_{\!\!,}\tilde ao~de~1^o~grau\\\sf basta~encontrar~dois~pontos:\\\sf\checkmark o~ponto~onde~o~gr\acute afico~intercepta~o~eixo~x\\\sf para~isso~fac_{\!\!,}a~y=0~e~resolva~a~equac_{\!\!,}\tilde ao~para~x\\\sf o~ponto~ser\acute a~da~forma~(x,0)~ou~(-x,0)\\\sf\checkmark o~ponto~onde~o~gr\acute afico~intercepta~o~eixo~y\\\sf para~isso~fac_{\!\!,}a~x=0~e~calcule~o~valor~de~y\\\sf o~ponto~ser\acute a~da~forma$

$\sf(0,y)~ou~(0,-y)$

$\Large\boxed{\begin{array}{l}\sf y=x-3\\\sf a=1>0\implies func_{\!\!,}\tilde ao~crescente\\\underline{\rm intersecc_{\!\!,}\tilde ao~do~gr\acute afico~com~o~eixo~x:}\\\sf y=0\\\sf x-3=0\\\sf x=3\\\sf o~ponto~\acute e~da~forma~A(3,0)\\\underline{\rm intersecc_{\!\!,}\tilde ao~do~gr\acute afico~com~o~eixo~y:}\\\sf x=0\\\sf y=0-3\\\sf y=-3\\\sf o~ponto~\acute e~da~forma~B(0,-3)\\\sf o~gr\acute afico~est\acute a~anexo\end{array}}$