Question

Para la siguiente función f(x)=x+19 realizar su grafica desde -5 hasta 7

Answer 1

Para poder graficar la ecuación reemplazaremos los valores de x

   $\begin{array}{c}\sf{\boldsymbol{\bigcirc\kern-8pt\triangleright}\:\:Cuando\ \blue{x = -5}}\\\\\sf{y=x+19}\\\\\sf{y=(-5)+19}\\\\\boxed{\sf{y=14}}\end{array}$           $\begin{array}{c}\sf{\boldsymbol{\bigcirc\kern-8pt\triangleright}\:\:Cuando\ \blue{x = -4}}\\\\\sf{y=x+19}\\\\\sf{y=(-4)+19}\\\\\boxed{\sf{y=15}}\end{array}$          $\begin{array}{c}\sf{\boldsymbol{\bigcirc\kern-8pt\triangleright}\:\:Cuando\ \blue{x = -3}}\\\\\sf{y=x+19}\\\\\sf{y=(-3)+19}\\\\\boxed{\sf{y=16}}\end{array}$

   $\begin{array}{c}\sf{\boldsymbol{\bigcirc\kern-8pt\triangleright}\:\:Cuando\ \blue{x = -2}}\\\\\sf{y=x+19}\\\\\sf{y=(-2)+19}\\\\\boxed{\sf{y=17}}\end{array}$           $\begin{array}{c}\sf{\boldsymbol{\bigcirc\kern-8pt\triangleright}\:\:Cuando\ \blue{x = -1}}\\\\\sf{y=x+19}\\\\\sf{y=(-1)+19}\\\\\boxed{\sf{y=18}}\end{array}$          $\begin{array}{c}\sf{\boldsymbol{\bigcirc\kern-8pt\triangleright}\:\:Cuando\ \blue{x = 1}}\\\\\sf{y=x+19}\\\\\sf{y=(1)+19}\\\\\boxed{\sf{y=20}}\end{array}$

   $\begin{array}{c}\sf{\boldsymbol{\bigcirc\kern-8pt\triangleright}\:\:Cuando\ \blue{x = 0}}\\\\\sf{y=x+19}\\\\\sf{y=(0)+19}\\\\\boxed{\sf{y=19}}\end{array}$              $\begin{array}{c}\sf{\boldsymbol{\bigcirc\kern-8pt\triangleright}\:\:Cuando\ \blue{x = 1}}\\\\\sf{y=x+19}\\\\\sf{y=(1)+19}\\\\\boxed{\sf{y=20}}\end{array}$            $\begin{array}{c}\sf{\boldsymbol{\bigcirc\kern-8pt\triangleright}\:\:Cuando\ \blue{x = 2}}\\\\\sf{y=x+19}\\\\\sf{y=(2)+19}\\\\\boxed{\sf{y=21}}\end{array}$

   $\begin{array}{c}\sf{\boldsymbol{\bigcirc\kern-8pt\triangleright}\:\:Cuando\ \blue{x = 3}}\\\\\sf{y=x+19}\\\\\sf{y=(3)+19}\\\\\boxed{\sf{y=22}}\end{array}$              $\begin{array}{c}\sf{\boldsymbol{\bigcirc\kern-8pt\triangleright}\:\:Cuando\ \blue{x = 4}}\\\\\sf{y=x+19}\\\\\sf{y=(4)+19}\\\\\boxed{\sf{y=23}}\end{array}$            $\begin{array}{c}\sf{\boldsymbol{\bigcirc\kern-8pt\triangleright}\:\:Cuando\ \blue{x = 5}}\\\\\sf{y=x+19}\\\\\sf{y=(5)+19}\\\\\boxed{\sf{y=24}}\end{array}$

   $\begin{array}{c}\sf{\boldsymbol{\bigcirc\kern-8pt\triangleright}\:\:Cuando\ \blue{x = 6}}\\\\\sf{y=x+19}\\\\\sf{y=(6)+19}\\\\\boxed{\sf{y=25}}\end{array}$             $\begin{array}{c}\sf{\boldsymbol{\bigcirc\kern-8pt\triangleright}\:\:Cuando\ \blue{x = 7}}\\\\\sf{y=x+19}\\\\\sf{y=(7)+19}\\\\\boxed{\sf{y=26}}\end{array}$

Ordenamos los valores en una tabla

                                                 $\begin{array}{c|c}\blue{\sf{x}}&\blue{\sf{y}}\\^{\rule{65 pt}{0.4pt}\hspace{-36}}\\\sf{-5}&\sf{14}\\\sf{-4}&\sf{15}\\\sf{-3}&\sf{16}\\\sf{-2}&\sf{17}\\\sf{-1}&\sf{18}\\\sf{1}&\sf{20}\\\sf{0}&\sf{19}\\\sf{1}&\sf{20}\\\sf{2}&\sf{21}\\\sf{3}&\sf{22}\\\sf{4}&\sf{23}\\\sf{5}&\sf{24}\\\sf{6}&\sf{25}\\\sf{7}&\sf{26}\\\end{array}$

Para graficar ubicamos nuestros puntos en un plano cartesiano y los unimos(ver imagen).

                                            $\boxed{\sf{{R}}\quad\raisebox{10pt}{ \sf{\red{O}} }\!\!\!\!\raisebox{-10pt}{ \sf{\red{O}} }\quad\raisebox{15pt}{ \sf{{G}} }\!\!\!\!\raisebox{-15pt}{ \sf{{G}} }\quad\raisebox{15pt}{ \sf{\red{H}} }\!\!\!\!\raisebox{-15pt}{ \sf{\red{H}} }\quad\raisebox{10pt}{ \sf{{E}} }\!\!\!\!\raisebox{-10pt}{ \sf{{E}} }\quad\sf{\red{R}}}\hspace{-64.5pt}\rule{10pt}{.2ex}\:\rule{3pt}{1ex}\rule{3pt}{1.5ex}\rule{3pt}{2ex}\rule{3pt}{1.5ex}\rule{3pt}{1ex}\:\rule{10pt}{.2ex}$