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Alterações para resolver problemas com imagens no html #23

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2bc433e
+script para converter svg para eps
fazedo Jul 13, 2022
297a405
+imagens em eps
fazedo Jul 13, 2022
1585257
uniformizar nome de script com outros
fazedo Jul 13, 2022
aa86af0
+script para remover tiks do texto e criar um standalone
fazedo Jul 18, 2022
f4187ff
+figuras de cap_funcao
fazedo Jul 18, 2022
53b7561
+figuras de cap_funcao
fazedo Jul 18, 2022
bfa0a2d
movi figuras tikz para arquivo standalone
fazedo Jul 18, 2022
3224060
Movi figuras tikz para arquivos standalone
fazedo Jul 18, 2022
2713511
+figuras que estavam como tikz no arquivo
fazedo Jul 18, 2022
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211 changes: 14 additions & 197 deletions cap_funcao/cap_funcao.tex
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Original file line number Diff line number Diff line change
Expand Up @@ -15,115 +15,29 @@ \chapter{Introdução às funções}

Exemplos de relações que são funções de $A$ em $B$:
\begin{multicols}{3}
\begin{tikzpicture}[scale=0.50]
\node (1) at (0,0) {1};%\filldraw(1.east) circle (1pt)
\node (2) [below of=1] {2};%\filldraw(2.east) circle (1pt)
\node (3) [below of=2] {3};%\filldraw(3.east) circle (1pt)
\node[fit=(1) (2) (3),ellipse,draw=red,minimum width=1cm,thick,label=below:\(A\)]{};

\node (a) at (3,0) {a};%\filldraw($b_1$.west) circle (1pt)
\node (b) [below of=a] {b};%\filldraw($b_2$.west) circle (1pt)
\node (c) [below of=b] {c};%\filldraw($b_3$.west) circle (1pt)
\node[fit=(a) (b) (c),ellipse,draw=green,minimum width=1cm,thick,label=below:\(B\)]{};

\draw[->, shorten >=.1cm, >=stealth'] (1.east) to (a.west);
\draw[->, shorten >=.1cm, >=stealth'] (2.east) to (b.west);
\draw[->, shorten >=.1cm, >=stealth'] (3.east) to (c.west);
\end{tikzpicture}

\begin{tikzpicture}[scale=0.50]
\node (1) at (0,0) {1};%\filldraw(1.east) circle (1pt)
\node (2) [below of=1] {2};%\filldraw(2.east) circle (1pt)
\node (3) [below of=2] {3};%\filldraw(3.east) circle (1pt)
\node[fit=(1) (2) (3),ellipse,draw=red,minimum width=1cm,thick,label=below:\(A\)]{};

\node (a) at (3,0) {a};%\filldraw($b_1$.west) circle (1pt)
\node (b) [below of=a] {b};%\filldraw($b_2$.west) circle (1pt)
\node (c) [below of=b] {c};%\filldraw($b_3$.west) circle (1pt)
\node[fit=(a) (b) (c),ellipse,draw=green,minimum width=1cm,thick,label=below:\(B\)]{};

\draw[->, shorten >=.1cm, >=stealth'] (1.east) to (a.west);
\draw[->, shorten >=.1cm, >=stealth'] (2.east) to (a.west);
\draw[->, shorten >=.1cm, >=stealth'] (3.east) to (c.west);
\end{tikzpicture}

\begin{tikzpicture}[scale=0.50]
\node (1) at (0,0) {1};%\filldraw(1.east) circle (1pt)
\node (2) [below of=1] {2};%\filldraw(2.east) circle (1pt)
\node (3) [below of=2] {3};%\filldraw(3.east) circle (1pt)
\node[fit=(1) (2) (3),ellipse,draw=red,minimum width=1cm,thick,label=below:\(A\)]{};

\node (a) at (3,0) {a};%\filldraw($b_1$.west) circle (1pt)
\node (b) [below of=a] {b};%\filldraw($b_2$.west) circle (1pt)
\node (c) [below of=b] {c};%\filldraw($b_3$.west) circle (1pt)
\node[fit=(a) (b) (c),ellipse,draw=green,minimum width=1cm,thick,label=below:\(B\)]{};

\draw[->, shorten >=.1cm, >=stealth'] (1.east) to (b.west);
\draw[->, shorten >=.1cm, >=stealth'] (2.east) to (b.west);
\draw[->, shorten >=.1cm, >=stealth'] (3.east) to (b.west);
\end{tikzpicture}
\includegraphics{cap_funcao/figs/tikz/figura_cap_funcao_1}

\includegraphics{cap_funcao/figs/tikz/figura_cap_funcao_2}

\includegraphics{cap_funcao/figs/tikz/figura_cap_funcao_3}

\end{multicols}

Exemplos de relações que não são funções de $A$ em $B$:
\begin{multicols}{2}
\begin{tikzpicture}[scale=0.50]
\node (1) at (0,0) {1};%\filldraw(1.east) circle (1pt)
\node (2) [below of=1] {2};%\filldraw(2.east) circle (1pt)
\node (3) [below of=2] {3};%\filldraw(3.east) circle (1pt)
\node[fit=(1) (2) (3),ellipse,draw=red,minimum width=1cm,thick,label=below:\(A\)]{};

\node (a) at (3,0) {a};%\filldraw($b_1$.west) circle (1pt)
\node (b) [below of=a] {b};%\filldraw($b_2$.west) circle (1pt)
\node (c) [below of=b] {c};%\filldraw($b_3$.west) circle (1pt)
\node[fit=(a) (b) (c),ellipse,draw=green,minimum width=1cm,thick,label=below:\(B\)]{};

\draw[->, shorten >=.1cm, >=stealth'] (1.east) to (a.west);
\draw[->, shorten >=.1cm, >=stealth'] (1.east) to (b.west);
\draw[->, shorten >=.1cm, >=stealth'] (2.east) to (b.west);
\draw[->, shorten >=.1cm, >=stealth'] (3.east) to (c.west);
\end{tikzpicture}
\includegraphics{cap_funcao/figs/tikz/figura_cap_funcao_4}

Não é função pois o elemento $1 \in A$ está relacionado aos elementos $a$ e $b$ do conjunto $B$.
\end{multicols}

\begin{multicols}{2}
\begin{tikzpicture}[scale=0.50]
\node (1) at (0,0) {1};%\filldraw(1.east) circle (1pt)
\node (2) [below of=1] {2};%\filldraw(2.east) circle (1pt)
\node (3) [below of=2] {3};%\filldraw(3.east) circle (1pt)
\node[fit=(1) (2) (3),ellipse,draw=red,minimum width=1cm,thick,label=below:\(A\)]{};

\node (a) at (3,0) {a};%\filldraw($b_1$.west) circle (1pt)
\node (b) [below of=a] {b};%\filldraw($b_2$.west) circle (1pt)
\node (c) [below of=b] {c};%\filldraw($b_3$.west) circle (1pt)
\node[fit=(a) (b) (c),ellipse,draw=green,minimum width=1cm,thick,label=below:\(B\)]{};

\draw[->, shorten >=.1cm, >=stealth'] (1.east) to (a.west);
%\draw[->, shorten >=.1cm, >=stealth'] (2.east) to (b.west);
\draw[->, shorten >=.1cm, >=stealth'] (3.east) to (c.west);
\end{tikzpicture}
\includegraphics{cap_funcao/figs/tikz/figura_cap_funcao_5}

Não é função pois o elemento $2 \in A$ não está relacionado com nenhum elemento do conjunto $B$.
\end{multicols}

\begin{multicols}{2}
\begin{tikzpicture}[scale=0.50]
\node (1) at (0,0) {1};%\filldraw(1.east) circle (1pt)
\node (2) [below of=1] {2};%\filldraw(2.east) circle (1pt)
\node (3) [below of=2] {3};%\filldraw(3.east) circle (1pt)
\node[fit=(1) (2) (3),ellipse,draw=red,minimum width=1cm,thick,label=below:\(A\)]{};

\node (a) at (3,0) {a};%\filldraw($b_1$.west) circle (1pt)
\node (b) [below of=a] {b};%\filldraw($b_2$.west) circle (1pt)
\node (c) [below of=b] {c};%\filldraw($b_3$.west) circle (1pt)
\node[fit=(a) (b) (c),ellipse,draw=green,minimum width=1cm,thick,label=below:\(B\)]{};

\draw[->, shorten >=.1cm, >=stealth'] (1.east) to (a.west);
\draw[->, shorten >=.1cm, >=stealth'] (1.east) to (b.west);
%\draw[->, shorten >=.1cm, >=stealth'] (2.east) to (b.west);
\draw[->, shorten >=.1cm, >=stealth'] (3.east) to (c.west);
\end{tikzpicture}
\includegraphics{cap_funcao/figs/tikz/figura_cap_funcao_6}

Não é função pois o elemento $1 \in A$ está relacionado aos elementos $a$ e $b$ do conjunto $B$ e o elemento $2 \in A$ não está relacionado com nenhum elemento do conjunto $B$
\end{multicols}
Expand Down Expand Up @@ -162,22 +76,7 @@ \chapter{Introdução às funções}

\begin{figure}[H]
\centering
\begin{tikzpicture}
\node (1) at (0,0) {1};%\filldraw(1.east) circle (1pt)
\node (2) [below of=1] {2};%\filldraw(2.east) circle (1pt)
\node (3) [below of=2] {3};%\filldraw(3.east) circle (1pt)
\node[fit=(1) (2) (3),ellipse,draw=red,minimum width=1cm,thick,label=below:\(A\)]{};

\node (a) at (3,0) {a};%\filldraw($b_1$.west) circle (1pt)
\node (b) [below of=a] {b};%\filldraw($b_2$.west) circle (1pt)
\node (c) [below of=b] {c};%\filldraw($b_3$.west) circle (1pt)
\node (d) [below of=c] {d};%\filldraw($b_3$.west) circle (1pt)
\node[fit=(a) (b) (c) (d),ellipse,draw=green,minimum width=1cm,thick,label=below:\(B\)]{};

\draw[->, shorten >=.1cm, >=stealth'] (1.east) to (b.west);
\draw[->, shorten >=.1cm, >=stealth'] (2.east) to (c.west);
\draw[->, shorten >=.1cm, >=stealth'] (3.east) to (a.west);
\end{tikzpicture}
\includegraphics{cap_funcao/figs/tikz/figura_cap_funcao_7}
\end{figure}

Note que esta regra define uma função $f: A \rightarrow B$, cujo domínio é $Dom(f) = A$, contra-domínio é $CDom(f) = B$, e a imagem é $Im(f)= \{a, b, c\}$, observe que $Im(f) \subset CDom(f)$. Pela definição, temos que o gráfico da $f$ será o conjunto
Expand Down Expand Up @@ -887,33 +786,7 @@ \section{Composição de funções}

\begin{figure}[H]
\centering
\begin{tikzpicture}
\centering
\node (1) at (0,0) {1};%\filldraw(1.east) circle (1pt)
\node (2) [below of=1] {2};%\filldraw(2.east) circle (1pt)
\node (3) [below of=2] {3};%\filldraw(3.east) circle (1pt)
\node[fit=(1) (2) (3),ellipse,draw=red,minimum width=1cm,thick,label=below:\(A\)]{};

\node (a) at (3,0) {a};%\filldraw($b_1$.west) circle (1pt)
\node (b) [below of=a] {b};%\filldraw($b_2$.west) circle (1pt)
\node (c) [below of=b] {c};%\filldraw($b_3$.west) circle (1pt)
\node (d) [below of=c] {d};%\filldraw($b_3$.west) circle (1pt)
\node[fit=(a) (b) (c) (d),ellipse,draw=green,minimum width=1cm,thick,label=below:\(B\)]{};

\node (A) at (6,0) {A};%\filldraw($b_1$.west) circle (1pt)
\node (B) [below of=A] {B};%\filldraw($b_2$.west) circle (1pt)
\node (C) [below of=B] {C};%\filldraw($b_3$.west) circle (1pt)
\node (D) [below of=C] {D};%\filldraw($b_3$.west) circle (1pt)
\node[fit=(A) (B) (C) (D),ellipse,draw=blue,minimum width=1cm,thick,label=below:\(C\)]{};

\draw[->, shorten >=.1cm, >=stealth'] (1.east) to (b.west);
\draw[->, shorten >=.1cm, >=stealth'] (2.east) to (c.west);
\draw[->, shorten >=.1cm, >=stealth'] (3.east) to (a.west);

\draw[->, shorten >=.1cm, >=stealth'] (a.east) to (A.west);
\draw[->, shorten >=.1cm, >=stealth'] (b.east) to (B.west);
\draw[->, shorten >=.1cm, >=stealth'] (c.east) to (C.west);
\end{tikzpicture}
\includegraphics{cap_funcao/figs/tikz/figura_cap_funcao_8}
\caption{Composição de funções}
\end{figure}

Expand Down Expand Up @@ -1166,40 +1039,13 @@ \section{Funções injetoras e/ou sobrejetoras}
\begin{multicols}{2}
\begin{figure}[H]
\centering
\begin{tikzpicture}
\node (1) at (0,0) {1};%\filldraw(1.east) circle (1pt)
\node (2) [below of=1] {2};%\filldraw(2.east) circle (1pt)
\node (3) [below of=2] {3};%\filldraw(3.east) circle (1pt)
\node[fit=(1) (2) (3),ellipse,draw=red,minimum width=1cm,thick,label=below:\(A\)]{};

\node (a) at (3,0) {a};%\filldraw($b_1$.west) circle (1pt)
\node (b) [below of=a] {b};%\filldraw($b_2$.west) circle (1pt)
\node (c) [below of=b] {c};%\filldraw($b_3$.west) circle (1pt)
\node[fit=(a) (b) (c),ellipse,draw=green,minimum width=1cm,thick,label=below:\(B\)]{};

\draw[->, shorten >=.1cm, >=stealth'] (1.east) to (c.west);
\draw[->, shorten >=.1cm, >=stealth'] (2.east) to (b.west);
\draw[->, shorten >=.1cm, >=stealth'] (3.east) to (a.west);
\end{tikzpicture}
\includegraphics{cap_funcao/figs/tikz/figura_cap_funcao_9}
\caption{Função bijetora}
\end{figure}

\begin{figure}[H]
\centering
\begin{tikzpicture}
\node (1) at (0,0) {1};%\filldraw(1.east) circle (1pt)
\node (2) [below of=1] {2};%\filldraw(2.east) circle (1pt)
\node (3) [below of=2] {3};%\filldraw(3.east) circle (1pt)
\node[fit=(1) (2) (3),ellipse,draw=red,minimum width=1cm,thick,label=below:\(A\)]{};

\node (a) at (3,0) {a};%\filldraw($b_1$.west) circle (1pt)
\node (b) [below of=a] {b};%\filldraw($b_2$.west) circle (1pt)
\node[fit=(a) (b),ellipse,draw=green,minimum width=1cm,thick,label=below:\(B\)]{};

\draw[->, shorten >=.1cm, >=stealth'] (1.east) to (a.west);
\draw[->, shorten >=.1cm, >=stealth'] (2.east) to (a.west);
\draw[->, shorten >=.1cm, >=stealth'] (3.east) to (b.west);
\end{tikzpicture}
\includegraphics{cap_funcao/figs/tikz/figura_cap_funcao_10}
\caption{Função sobrejetora e não injetora}
\end{figure}
\end{multicols}
Expand All @@ -1208,42 +1054,13 @@ \section{Funções injetoras e/ou sobrejetoras}
\begin{multicols}{2}
\begin{figure}[H]
\centering
\begin{tikzpicture}
\node (1) at (0,0) {1};%\filldraw(1.east) circle (1pt)
\node (2) [below of=1] {2};%\filldraw(2.east) circle (1pt)
\node (3) [below of=2] {3};%\filldraw(3.east) circle (1pt)
\node[fit=(1) (2) (3),ellipse,draw=red,minimum width=1cm,thick,label=below:\(A\)]{};

\node (a) at (3,0) {a};%\filldraw($b_1$.west) circle (1pt)
\node (b) [below of=a] {b};%\filldraw($b_2$.west) circle (1pt)
\node (c) [below of=b] {c};%\filldraw($b_3$.west) circle (1pt)
\node[fit=(a) (b) (c),ellipse,draw=green,minimum width=1cm,thick,label=below:\(B\)]{};

\draw[->, shorten >=.1cm, >=stealth'] (1.east) to (b.west);
\draw[->, shorten >=.1cm, >=stealth'] (2.east) to (b.west);
\draw[->, shorten >=.1cm, >=stealth'] (3.east) to (a.west);
\end{tikzpicture}
\includegraphics{cap_funcao/figs/tikz/figura_cap_funcao_11}
\caption{Função não sobrejetora e não injetora}
\end{figure}

\begin{figure}[H]
\centering
\begin{tikzpicture}
\node (1) at (0,0) {1};%\filldraw(1.east) circle (1pt)
\node (2) [below of=1] {2};%\filldraw(2.east) circle (1pt)
\node (3) [below of=2] {3};%\filldraw(3.east) circle (1pt)
\node[fit=(1) (2) (3),ellipse,draw=red,minimum width=1cm,thick,label=below:\(A\)]{};

\node (a) at (3,0) {a};%\filldraw($b_1$.west) circle (1pt)
\node (b) [below of=a] {b};%\filldraw($b_2$.west) circle (1pt)
\node (c) [below of=b] {c};%\filldraw($b_3$.west) circle (1pt)
\node (d) [below of=c] {d};%\filldraw($b_3$.west) circle (1pt)
\node[fit=(a) (b) (c) (d),ellipse,draw=green,minimum width=1cm,thick,label=below:\(B\)]{};

\draw[->, shorten >=.1cm, >=stealth'] (1.east) to (b.west);
\draw[->, shorten >=.1cm, >=stealth'] (2.east) to (c.west);
\draw[->, shorten >=.1cm, >=stealth'] (3.east) to (a.west);
\end{tikzpicture}
\includegraphics{cap_funcao/figs/tikz/figura_cap_funcao_7}
\caption{Função não sobrejetora e injetora}
\end{figure}
\end{multicols}
Expand Down
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