Question

Seja a função f: R -> R tal que f(x) = ax - 3. Se -2 é zero da função, qual é o valor de f(2)?

Answer 1

No gráfico, temos que a = -2

 

Então temos fuma no função: f(x) = -2x - 3

 

Logo f(2) = -2.2 -3

f(2) = -4-3

$\Large\text{ \boxed{\blue{f(2)=-7}} }$

Answer 2

$\boxed{\begin{array}{l}\underline{\rm De~\!\!finic_{\!\!,}\tilde ao\,de\,func_{\!\!,}\tilde ao\,de\,1^o\,grau}\\\sf Chama-se\,func_{\!\!,}\tilde ao\,de\,1^o\,grau\,a\,toda\,func_{\!\!,}\tilde ao\\\sf f:\mathbb{R}\longrightarrow\mathbb{R}~de~\!\!finida\,por\,f(x)=ax+b~ou~y=ax+b\\\sf com\,a\ne0. \end{array}}$

$\boxed{\begin{array}{l}\sf~se~f(x)=ax+b\\\sf a\longrightarrow coeficiente\,angular\\\sf b\longrightarrow coeficiente\,linear.\\\underline{\bf ra\acute iz\,ou\,zero\,da\,func_{\!\!,}\tilde ao:}\\\sf S\tilde ao\,os\,valores\,de\,x\,que\,anulam\,a\,func_{\!\!,}\tilde ao.\\\sf como~f(x)=ax+b \\\sf ent\tilde ao~ax+b=0\\\sf ax=-b\\\sf x=-\dfrac{b}{a}\end{array}}$

$\large\boxed{\begin{array}{l}\sf isto\,\acute e\,a\,ra\acute iz\,da\,func_{\!\!,}\tilde ao\,\,de\,1^o\,grau\\\sf \acute e\,o\,contr\acute ario\\\sf do\,coeficiente\,linear\\\sf dividido\,pelo\,coeficiente\,angular\end{array}}$

$\large\boxed{\begin{array}{l}\sf f(x)=ax-3\\\underline{\bf zero\,da\,func_{\!\!,}\tilde ao\!:}\\\sf x=-\dfrac{-3}{a}=\dfrac{3}{a}\\\sf o\,exerc\acute icio\,afirma\,que~-2\,\acute e\,zero\,da\,func_{\!\!,}\tilde ao\\\sf ou\,seja~x=-2.~Substituindo\,temos:\\\sf -2=\dfrac{3}{a}\\\sf -2a=3\cdot(-1)\\\sf 2a=-3\\\sf a=-\dfrac{3}{2}\\\sf f(x)=-\dfrac{3}{2}x-2\\\\\sf f(2)=-\dfrac{3}{\backslash\!\!\!2}\cdot\backslash\!\!\!2-2\\\sf f(2)=-3-2\\\sf f(2)=-5\end{array}}$