Ένα σχήμα την ημέρα

Η αλήθεια είναι ότι ένα από τα πιο όμορφα, χρήσιμα και περίπλοκα πράγματα με το \LaTeX είναι το tikz. Αν τυχαίνει να μην το γνωρίζετε – που ίσως να είναι και ευχής έργον να μην το γνωρίζετε – το tikz είναι ένα πακέτο ανάπτυξης γραφικών που υποστηρίζεται από το \LaTeX. Τις «οδηγίες χρήσης» του tikz μπορείτε να τις βρείτε ελεύθερα εδώ – τη στιγμή που αυτή η πρόταση γράφεται, είναι μόλις 1321 σελίδες. Η αλήθεια είναι ότι την πρώτη φορά που χρειάστηκε να στοιχειοθετήσω κάποιο σχήμα χρησιμοποιώντας το tikz απλά έψαξα για άλλες εναλλακτικές, καθώς οι τότε περίπου 1200 σελίδες του εγχειριδίου χρήσης ήταν τουλάχιστον αποθαρρυντικές.

Αλλά, έρχεται η μέρα που θες να κάνεις κάτι περίπλοκο που το GeoGebra ή διάφορα άλλα εργαλεία δεν μπορούν να κάνουν κομψά και απλά ή, εν πάση περιπτώσει, η ζωή τα φέρνει έτσι που το tikz είναι μονόδρομος. Το να διαβάσει κανείς όμως τις οδηγίες χρήσης δεν είναι. Υπάρχουν παραδείγματα στο διαδίκτυο και ερωτήσεις – ειδικά στο αξιαγάπητο tex.stackexchange.com, οι οποίες καλύπτουν και τις πιο μύχιες επιθυμίες μας (σχεδόν). Μετά από αρκετά χρόνια ενασχόλησης, και μιας και όλη αυτή τη γνώση την πήρα δωρεάν, είπα να την επιστρέψω σχεδόν όπως την πήρα. Σε αυτήν τη στήλη θα βρίσκετε σχήματα στοιχειοθετημένα με tikz καθώς και τον πηγαίο κώδικά τους – αν υπάρχει όρεξη, ίσως και κάποια σχόλια σε σχέση με αυτόν.

Καλή ανάγνωση! 🙂

Για περισσότερα για κάθε σχήμα, μπορείτε να δείτε και τις δημοσιεύσεις σε αυτήν την κατηγορία.


Μετατόπιση…

\documentclass[tikz, margin=5mm]{standalone}
\usepackage{ifthen}

\usetikzlibrary{intersections}

\begin{document}
	\begin{tikzpicture}
	\draw[thick,->,name path=x axis] (-4,0) -- (4,0)node[pos=1,below]{$x$};
	\draw[thick,->,name path=y axis] (0,-2.5) -- (0,3)node[pos=1,left]{$y$};
	\node[left,yshift=-8pt](O) at (0,0){$O$};
	\begin{scope}
	\clip (-5,-3) rectangle (5,3.3);
	\draw[very thick, name path=curve 1, red] (-3,-2) .. controls (-1,3) and (2,-3) .. (3,0)node[pos=.8,below]{$f(x)+c,\ c<0$};
	\draw[name path=curve 2, blue!50!black] (-3,-1) .. controls (-1,4) and (2,-2) .. (3,1)node[pos=1,right]{$f$};
	\draw[very thick, name path=curve 3, green!40!black] (-3,.5) .. controls (-1,5.5) and (2,-.5) .. (3,2.5)node[pos=1,above]{$f(x)+c,\ c>0$};
	\foreach \i in {-3,...,3}{
		\draw[draw=none, name path=line \i] (\i,-4) -- (\i,4);
		\node[inner sep=0pt, outer sep=0pt, name intersections={of={curve 1 and line \i}}](A\i) at (intersection-1){};
		\node[inner sep=0pt, outer sep=0pt, name intersections={of={curve 2 and line \i}}](B\i) at (intersection-1){};
		\node[inner sep=0pt, outer sep=0pt, name intersections={of={curve 3 and line \i}}](C\i) at (intersection-1){};
		\ifthenelse{\i=-3}{
			\draw[orange, <->] (A\i) -- (B\i)node[pos=.5,left]{$c$};
			\draw[orange, <->] (B\i) -- (C\i)node[pos=.5,left]{$c$};
		}
		{
			\draw[orange, <->] (A\i) -- (B\i)node[pos=.5,right]{$c$};
			\draw[orange, <->] (B\i) -- (C\i)node[pos=.5,right]{$c$};
		}
	}
	\end{scope}
	\end{tikzpicture}
\end{document}

Περιττό…

\documentclass[tikz, margin=5mm]{standalone}

\usetikzlibrary{calc}
\usetikzlibrary{intersections}

\begin{document}
	\begin{tikzpicture}
	\draw[thick,->,name path=x axis] (-4,0) -- (4,0)node[pos=1,below]{$x$};
	\draw[thick,->,name path=y axis] (0,-3) -- (0,3)node[pos=1,left]{$y$};
	\node[left,yshift=-8pt](O) at (0,0){$O$};
	\begin{scope}
	\clip (-4,-3) rectangle (4,3);
	\draw[thick, name path=curve 1, blue!50!black] (-3.6,-1) .. controls (-2,4) and (-1,3) .. (0,0);
	\draw[thick, name path=curve 2, blue!50!black] (3.6,1) .. controls (2,-4) and (1,-3) .. (0,0)node[pos=0,above]{$f$};
	\node[circle, fill=black, inner sep=1pt, label={above}:{$\textcolor{green!40!black}{x}$}](x) at (2.6,0){};
	\node[circle, fill=black, inner sep=1pt, label={below}:{$\textcolor{green!40!black}{-x}$}](mx) at (-2.6,0){};
	\draw[draw=none, name path=line 2] (2.6,-4) -- (2.6,4);
	\draw[draw=none, name path=line 1] (-2.6,-4) -- (-2.6,4);
	\node[circle, fill=green!40!black, inner sep=1pt, name intersections={of={line 1 and curve 1}}](A) at (intersection-1){};
	\node[circle, fill=green!40!black, inner sep=1pt, name intersections={of={line 2 and curve 2}}](B) at (intersection-1){};
	\end{scope}
	\draw[dashed,->,orange] (x) -- (B);
	\draw[dashed,->,orange] (mx) -- (A);
	\draw[dashed,<->,orange] (A) -- (B);
	\draw[dashed,->,orange] (B) -- ($(0,-4)!(B)!(0,4)$)node[pos=1,left]{$f(x)$};
	\draw[dashed,->,orange] (A) -- ($(0,-4)!(A)!(0,4)$)node[pos=1,right]{$-f(x)=f(-x)$};
	\end{tikzpicture}
\end{document}

Άρτιο…

\documentclass[tikz, margin=5mm]{standalone}

\usetikzlibrary{intersections}

\begin{document}
	\begin{tikzpicture}
	\draw[thick,->,name path=x axis] (-4,0) -- (4,0)node[pos=1,below]{$x$};
	\draw[thick,->,name path=y axis] (0,-2) -- (0,4)node[pos=1,left]{$y$};
	\node[left,yshift=-8pt](O) at (0,0){$O$};
	\draw[thick, name path=curve 1, blue!50!black] (-3.6,2.5) .. controls (-2,-4) and (-1,3) .. (0,1);
	\draw[thick, name path=curve 2, blue!50!black] (3.6,2.5) .. controls (2,-4) and (1,3) .. (0,1)node[pos=0,above]{$f$};
	\node[circle, fill=black, inner sep=1pt, green!40!black, label={below}:{$\textcolor{green!40!black}{x}$}](x) at (3.4,0){};
	\node[circle, fill=black, inner sep=1pt, green!40!black, label={below}:{$\textcolor{green!40!black}{-x}$}](mx) at (-3.4,0){};
	\draw[draw=none, name path=line 2] (3.4,-4) -- (3.4,4);
	\draw[draw=none, name path=line 1] (-3.4,-4) -- (-3.4,4);
	\node[circle, fill=green!40!black, inner sep=1pt, name intersections={of={line 1 and curve 1}}](A) at (intersection-1){};
	\node[circle, fill=green!40!black, inner sep=1pt, name intersections={of={line 2 and curve 2}}](B) at (intersection-1){};
	\draw[dashed,->,orange] (x) -- (B);
	\draw[dashed,->,orange] (mx) -- (A);
	\draw[dashed,<->,orange] (A) -- (B)node[pos=.5,right,yshift=8pt]{$f(x)=f(-x)$};
	\end{tikzpicture}
\end{document}

Ανισότητες…

\documentclass[tikz, margin=5mm]{standalone}

\usetikzlibrary{calc}
\usetikzlibrary{intersections}

\begin{document}
	\begin{tikzpicture}
	\draw[thick,->,name path=x axis] (-4,0) -- (4,0)node[pos=1,below]{$x$};
	\draw[thick,->,name path=y axis] (0,-2.7) -- (0,3)node[pos=1,left]{$y$};
	%\node[left,yshift=-8pt](O) at (0,0){$O$};
	\draw[very thick, blue!75!black, name path=curve 1, samples=200] (-3,-2) .. controls (-.5,2) and (2,-2.7) .. (3,1) node[pos=1,right]{$f$};
	\draw[very thick, red, name path=curve 2, samples=200] (-3,3) .. controls (-2,-2.7) and (2.2,3) .. (3,3) node[pos=1,right]{$g$};
	\foreach \i in {-3,-2.8,...,3.1}{
		\draw[draw=none, name path=line \i] (\i,-3) -- (\i,3);
		\pgfmathtruncatemacro{\res}{20*\i}
		\node[draw=none, outer sep=0pt, inner sep=0pt, name intersections={of={curve 1 and line \i}}](A\res) at (intersection-1){};
		\node[draw=none, outer sep=0pt, inner sep=0pt, name intersections={of={curve 2 and line \i}}](B\res) at (intersection-1){};
		\draw[orange, <->] (A\res) -- (B\res);
	}
	\end{tikzpicture}
\end{document}

Πιο σύνθετα πράγματα…

\documentclass[tikz, margin=5mm]{standalone}

\usetikzlibrary{calc}
\usetikzlibrary{intersections}

\begin{document}
	\begin{tikzpicture}
	\draw[thick] (0,0) ellipse (1.2 and 1.9)node[yshift=-2.2cm,xshift=-1cm]{$A$};
	\draw[thick] (3,0) ellipse (1.2 and 1.9)node[yshift=-2.2cm,xshift=-1cm]{$B\cup C$};
	\draw[thick] (6,0) ellipse (1.2 and 1.9)node[yshift=-2.2cm,xshift=-1cm]{$D$};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={left}:{$a$}](a) at (.4,1.2){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={left}:{$b$}](b) at (-.4,.4){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={left}:{$c$}](c) at (.5,-.4){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={left}:{$d$}](d) at (-.3,-1.2){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={above}:{$1$}](1) at (3.3,1.2){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={above}:{$2$}](2) at (2.5,.4){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={above}:{$3$}](3) at (3.4,-.4){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={above}:{$4$}](4) at (2.6,-1.2){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={right}:{$e$}](e) at (6.3,1.2){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={right}:{$f$}](f) at (5.5,.4){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={right}:{$g$}](g) at (6.4,-.4){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={right}:{$h$}](h) at (5.6,-1.2){};
	\draw[thick,->,blue!75!black] (a) -- (2);
	\draw[thick,->,blue!75!black] (b) -- (3);
	\draw[thick,->,blue!75!black] (c) -- (3);
	\draw[thick,->,blue!75!black] (d) -- (4);
	\draw[thick,->,red] (1) -- (f);
	\draw[thick,->,red] (2) -- (e);
	\draw[thick,->,red] (3) -- (h);
	%ASSIST NODES
	\node[draw=none](a1) at ($(1)+(.1,.3)$){};
	\node[draw=none](a2) at ($(2)+(-.2,0)$){};
	\node[draw=none](a3) at ($(3)+(.1,0)$){};
	\node[draw=none](a22) at ($(2)+(-.2,.4)$){};
	\node[draw=none](a4) at ($(4)+(0,-.1)$){};
	\node[draw=none](aa) at ($(a)+(0,.1)$){};
	\node[draw=none](ab) at ($(b)+(-.4,0)$){};
	\node[draw=none](ac) at ($(c)+(.1,-.1)$){};
	\draw[dashed, red, thick, fill=red, fill opacity=.1] plot [smooth cycle, tension=1] coordinates {(a1.north) (a2.west) (a3.south east)};
	\draw[dashed, blue!75!black, thick, fill=blue!75!black, fill opacity=.1] plot [smooth cycle, tension=1] coordinates {(a22.north) (a3.east) (a4.south west)};
	\draw[dashed, purple!75!black, thick, fill=purple!75!black, fill opacity=.1] plot [smooth cycle, tension=1] coordinates {(aa.north) (ab.west) (ac.south east)};
	\node[label={above,yshift=2pt}:{$\textcolor{red}{D_g}$}] at (a1){};
	\node[label={below,xshift=-20pt}:{$\textcolor{blue!75!black}{f(A)}$}] at (a4){};
	\node[label={left,xshift=-6pt}:{$\textcolor{purple!75!black}{D_{g\circ f}}$}] at (ab){};
	\end{tikzpicture}
\end{document}

Σύνθετα πράγματα…

\documentclass[tikz, margin=5mm]{standalone}

\usetikzlibrary{calc}
\usetikzlibrary{intersections}

\begin{document}
	\begin{tikzpicture}
	\draw[thick] (0,0) ellipse (1.2 and 1.9)node[yshift=-2.4cm,xshift=-1cm]{$A$};
	\draw[thick] (3,0) ellipse (1.2 and 1.9)node[yshift=-2.4cm,xshift=-1cm]{$B\cup C$};
	\draw[thick] (6,0) ellipse (1.2 and 1.9)node[yshift=-2.4cm,xshift=-1cm]{$D$};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={left}:{$a$}](a) at (.4,1.2){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={left}:{$b$}](b) at (-.4,.4){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={left}:{$c$}](c) at (.5,-.4){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={left}:{$d$}](d) at (-.3,-1.2){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={above}:{$1$}](1) at (3.3,1.2){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={above}:{$2$}](2) at (2.5,.4){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={above}:{$3$}](3) at (3.4,-.4){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={above}:{$4$}](4) at (2.6,-1.2){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={right}:{$e$}](e) at (6.3,1.2){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={right}:{$f$}](f) at (5.5,.4){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={right}:{$g$}](g) at (6.4,-.4){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={right}:{$h$}](h) at (5.6,-1.2){};
	\draw[thick,->,blue!75!black] (a) -- (2);
	\draw[thick,->,blue!75!black] (b) -- (3);
	\draw[thick,->,blue!75!black] (c) -- (3);
	\draw[thick,->,blue!75!black] (d) -- (4);
	\draw[thick,->,red] (1) -- (f);
	\draw[thick,->,red] (2) -- (e);
	\draw[thick,->,red] (3) -- (h);
	%ASSIST NODES
	\node[draw=none](a1) at ($(1)+(.1,.3)$){};
	\node[draw=none](a2) at ($(2)+(-.2,0)$){};
	\node[draw=none](a3) at ($(3)+(.1,0)$){};
	\node[draw=none](a22) at ($(2)+(-.2,.4)$){};
	\node[draw=none](a4) at ($(4)+(0,-.1)$){};
	\draw[dashed, red, thick, fill=red, fill opacity=.1] plot [smooth cycle, tension=1] coordinates {(a1.north) (a2.west) (a3.south east)};
	\draw[dashed, blue!75!black, thick, fill=blue!75!black, fill opacity=.1] plot [smooth cycle, tension=1] coordinates {(a22.north) (a3.east) (a4.south west)};
	\node[label={above,yshift=2pt}:{$\textcolor{red}{D_g}$}] at (a1){};
	\node[label={below,xshift=-20pt}:{$\textcolor{blue!75!black}{f(A)}$}] at (a4){};
	\end{tikzpicture}
\end{document}

Υπερβολές…

\documentclass[tikz, margin=5mm]{standalone}
\usepackage[english, greek]{babel}
\usepackage[iso-8859-7]{inputenc}

\pgfdeclarelayer{bg}
\pgfsetlayers{bg,main}

\usetikzlibrary{patterns}
\usetikzlibrary{intersections}

\begin{document}
	\begin{tikzpicture}
	\draw[thick,->,name path=x axis] (-2,0) -- (2,0)node[pos=1,below]{$x$};
	\draw[thick,->,name path=y axis] (0,-2) -- (0,2)node[pos=1,left]{$y$};
	\node[left,yshift=-8pt](O) at (0,0){$O$};
	\draw[thick, name path=line, samples=200, domain=-1.8:{-1/1.8}, color=blue!50!black] plot (\x,{.9/\x});
	\draw[thick, name path=line, samples=200, domain={1/1.8}:1.8, color=blue!50!black] plot (\x,{.9/\x});
	\node[color=blue!50!black] at (-1,1){$\displaystyle f(x)=\frac{a}{x}$};
	\node[circle, fill=orange, inner sep=1pt](A) at (1.2,{.9/1.2}){};
	\draw[->, color=green!40!black] (0,0) -- (A);
	\begin{pgfonlayer}{bg}
	\fill[pattern=north west lines, pattern color=orange] (0,0) rectangle (A);
	\node[orange](tab) at (1,-.5){Εμβ.=$a$};
	\end{pgfonlayer}
	\end{tikzpicture}
\end{document}

Μία ρίζα…

\documentclass[tikz, margin=5mm]{standalone}

\pgfdeclarelayer{bg}
\pgfsetlayers{bg,main}

\usetikzlibrary{calc}
\usetikzlibrary{intersections}

\begin{document}
	\begin{tikzpicture}
	\draw[thick,->,name path=x axis] (-1,0) -- (3,0)node[pos=1,below]{$x$};
	\draw[thick,->,name path=y axis] (0,-2) -- (0,2)node[pos=1,left]{$y$};
	\node[left,yshift=-8pt](O) at (0,0){$O$};
	\draw[thick, name path=line, samples=200, domain=0:2.7, color=blue!50!black] plot (\x,{.9*sqrt(\x)});
	\node[color=blue!50!black] at (1.2,-1){$f(x)=a\sqrt{x}$};
	\draw[draw=none, name path=curve] (1,-2) -- (1,2);
	\node[circle, fill=orange, inner sep=1pt, name intersections={of={curve and line}}](A) at (intersection-1){};
	\begin{pgfonlayer}{bg}
	\draw[dashed, orange] (0,0) rectangle (A);
	\end{pgfonlayer}
	\node[left, orange] at ($(0,-2)!(A)!(0,2)$){$a$};
	\node[below, orange] at (1,0){$1$};
	\end{tikzpicture}
\end{document}

Μία απλή απόλυτη τιμή…

\documentclass[tikz, margin=5mm]{standalone}

\pgfdeclarelayer{bg}
\pgfsetlayers{bg,main}

\usetikzlibrary{calc}
\usetikzlibrary{intersections}

\begin{document}
	\begin{tikzpicture}
	\draw[thick,->,name path=x axis] (-2,0) -- (2,0)node[pos=1,below]{$x$};
	\draw[thick,->,name path=y axis] (0,-2) -- (0,2)node[pos=1,left]{$y$};
	\node[left,yshift=-8pt](O) at (0,0){$O$};
	\draw[thick, name path=line, color=blue!50!black] (0,0) -- (1.8,1.4)node[pos=1,above]{$f(x)=a|x|$};
	\draw[thick, color=blue!50!black] (0,0) -- (-1.8,1.4);
	\draw[draw=none, name path=curve] (1,-2) -- (1,2);
	\node[circle, fill=orange, inner sep=1pt, name intersections={of={line and curve}}](A) at (intersection-1){};
	\begin{pgfonlayer}{bg}
	\draw[dashed, orange] (0,0) rectangle (A);
	\end{pgfonlayer}
	\node[left, orange] at ($(0,-2)!(A)!(0,2)$){$a$};
	\node[below, orange] at (1,0){$1$};
	\end{tikzpicture}
\end{document}

Πολλά μαζεύτηκαν εδώ…

\documentclass[tikz, margin=5mm]{standalone}

\usetikzlibrary{calc}
\usetikzlibrary{intersections}

\pgfdeclarelayer{bg}
\pgfsetlayers{bg,main}

\begin{document}
	\begin{tikzpicture}
	\fill[blue!5] (-4,-4) -- (4,4) -- (-4,4) -- cycle node[black, pos=.3, xshift=1cm]{$U$};
	\fill[red!5] (-4,-4) -- (4,4) -- (4,-4) -- cycle;
	\draw[draw=none, name path=bisectrix] (-4,-4) -- (4,4);
	\node[inner sep=0pt, outer sep=0pt](a) at (-2.4,2.7){};
	\draw[draw=none, name path={x-coord}] ($(-4,4)!(a)!(4,4)$) -- ($(-4,-4)!(a)!(4,-4)$);
	\draw[draw=none, name path={y-coord}] ($(-4,-4)!(a)!(-4,4)$) -- ($(4,-4)!(a)!(4,4)$);
	\draw[name intersections={of=bisectrix and y-coord}] (intersection-1) coordinate (b);
	\draw[name intersections={of=bisectrix and x-coord}] (intersection-1) coordinate (c);
	\fill[blue!15] (a) -- (c) -- (b) -- cycle;
	\fill[red!15] ($(-4,-4)!(a)!(4,-4)$) -- (c) -- (b) -- ($(4,-4)!(a)!(4,4)$) -- (4,-4) -- cycle node[black, pos=.3, yshift=2cm]{$L$};
	\draw[thick, ->] (-4,0) -- (4,0)node[pos=1,below]{$x$};
	\draw[thick, ->] (0,-4) -- (0,4)node[pos=1,left]{$y$};
	\draw[thick] (-4,-4) -- (4,4);
	\node[circle, inner sep=1.5pt, draw=black, fill=black, label={above}:{$A(a,f(a))$}](a-visible) at (a){};
	\node[circle, inner sep=1.5pt, draw=black, fill=black, label={above, xshift=-.85cm}:{$B(f(a),f(a))$}](b-visible) at (b){};
	\node[circle, inner sep=1.5pt, draw=black, fill=black, label={right}:{$C(a,a)$}](c-visible) at (c){};
	\draw[dashed, thick] ($(-4,-4)!(a)!(4,-4)$) -- (a) -- ($(4,-4)!(a)!(4,4)$);
	\node[draw=none, outer sep=0pt, inner sep=0pt](b-right-shift) at ($(b)+(.5,0)$){};
	\draw[thick, <->, red] (b-right-shift) -- ($(-4,-4)!(b-right-shift)!(4,-4)$);
	\node[circle, inner sep=1.5pt, draw=black, fill=black, label={left,yshift=-8pt}:{$f(a)+1$}](d) at ($(-4,0)!(b-right-shift)!(4,0)$){};
	\end{tikzpicture}
\end{document}

Ρίζες…

\documentclass[tikz, margin=5mm]{standalone}

\usepackage{ifthen}

\usetikzlibrary{calc}
\usetikzlibrary{intersections}

\begin{document}
	\begin{tikzpicture}
	\draw[thick,->,name path=x axis] (-4,0) -- (4,0)node[pos=1,below]{$x$};
	\draw[thick,->,name path=y axis] (0,-3) -- (0,3)node[pos=1,left]{$y$};
	\node[left,yshift=-8pt](O) at (0,0){$O$};
	\foreach \i in {-3,-2,...,3}{
	    \ifthenelse{\i=-3 \OR \i=3}{
	        \draw (\i,-.1) -- (\i,.1) node[pos=0,below]{};
	    }
	    {
	        \ifthenelse{\NOT \i=0}{
	            \draw (\i,-.1) -- (\i,.1) node[pos=0,below]{};
	            \draw (-.1,\i) -- (.1,\i) node[pos=0,left]{};
	        }{}
	    }
	}
	\draw[thick,green!40!black] (-4,0) -- (3.9,0)node[pos=1,above]{$y=0$};
	\draw[thick, name path=curve, color=blue!50!black] (-3,-1.5) .. controls (-1.9,3) and (2.6,-3) .. (3,2);
	\foreach \i in {1,2,3}{
	    \node[circle, fill=orange, inner sep=1pt, name intersections={of={curve and x axis}}] (A\i) at (intersection-\i){};
	}
	\coordinate (O) at (0,0);
	\coordinate (X) at (1,1);
	\path let \p1=($ (X) -(O) $),\p2=($ (A1) - (O)$),\n1={\x2/\x1} in
	node at ($(A1)+(0,.5)$){$\textcolor{orange}{x_1\approx\pgfmathroundtozerofill{\n1}\pgfmathresult}$};
	
	\path let \p1=($ (X) -(O) $),\p2=($ (A2) - (O)$),\n1={\x2/\x1} in
	node at ($(A2)+(.4,.5)$){$\textcolor{orange}{x_2\approx\pgfmathroundtozerofill{\n1}\pgfmathresult}$};
	
	\path let \p1=($ (X) -(O) $),\p2=($ (A3) - (O)$),\n1={\x2/\x1} in
	node at ($(A3)+(0,-.5)$){$\textcolor{orange}{x_3\approx\pgfmathroundtozerofill{\n1}\pgfmathresult}$};
	\end{tikzpicture}
\end{document}

Σύνθεση συναρτήσεων!

\documentclass[tikz, margin=5mm]{standalone}

\usepackage{amsmath}

\pgfdeclarelayer{bg}
\pgfsetlayers{bg,main}

\begin{document}
	\begin{tikzpicture}
	\node(x) at (-.5,0) {$\dfrac{\pi}{6}$};
	\node(gx) at (1,0) {$g\left(\dfrac{\pi}{6}\right)$};
	\node[right](fgx) at (2,0) {$f\left(g\left(\dfrac{\pi}{6}\right)\right)$};
	\draw[blue,|->] (x) -- (gx)node[pos=.5,above]{$\textcolor{blue}{g}$};
	\draw[red,|->] (gx) -- (fgx)node[pos=.5,above]{$\textcolor{red}{f}$};
	\end{tikzpicture}
\end{document}

Παράξενη καμπύλη…

\documentclass[tikz, margin=5mm]{standalone}

\pgfdeclarelayer{bg}
\pgfsetlayers{bg,main}

\begin{document}
	\begin{tikzpicture}
	\draw[thick,->] (-4,0) -- (4,0)node[pos=1,below]{$x$};
	\draw[thick,->] (0,-2.7) -- (0,3)node[pos=1,left]{$y$};
	\begin{scope}
	\clip (-4,-2.7) rectangle (4,3);
	\draw[thick,blue!50!black, domain={.5}:{3}, samples=100] (1,-2) .. controls (-6,2) and (2,2) .. (2,-1.85);
	\end{scope}
	\end{tikzpicture}
\end{document}

Το πεδίο ορισμού ως προβολή στο οριζόντιο άξονα…

\documentclass[tikz, margin=5mm]{standalone}

\usetikzlibrary{calc}
\usetikzlibrary{intersections}

\pgfdeclarelayer{bg}
\pgfsetlayers{bg,main}

\begin{document}
	\begin{tikzpicture}
	\draw[thick,->] (-4,0) -- (4,0)node[pos=1,below]{$x$};
	\draw[thick,->] (0,-2.7) -- (0,3)node[pos=1,left]{$y$};
	\begin{scope}
	\clip (-4,-2.7) rectangle (4,3);
	\draw[thick,blue!50!black, domain={.5}:{3}, samples=100, name path global=curve 1] plot (\x,{2/(\x+.5)});
	\draw[thick,blue!50!black, domain={-3}:{-1}, samples=100, name path global=curve 2] plot (\x,{1.5+\x});
	\end{scope}
	\foreach \i in {-2.78,-2.54,...,-1}{
		\pgfmathtruncatemacro{\coord}{100*\i}
		\draw[draw=none, name path=line \coord] (\i,-2.7) -- (\i,3);
		\node[draw=none, name intersections={of=curve 2 and line \coord},inner sep=0pt](a\coord) at (intersection-1){};
		\draw[orange,<-] ($(-4,0)!(a\coord)!(4,0)$) -- (a\coord);
	}
	\foreach \i in {.72,.94,...,3}{
		\pgfmathtruncatemacro{\coord}{100*\i}
		\draw[draw=none, name path=line \coord] (\i,-2.7) -- (\i,3);
		\node[draw=none, name intersections={of=curve 1 and line \coord},inner sep=0pt](a\coord) at (intersection-1){};
		\draw[orange,<-] ($(-4,0)!(a\coord)!(4,0)$) -- (a\coord);
	}
	\node[circle, inner sep=1pt, fill=blue!50!black, draw=blue!50!black, label={left}:{$\scriptstyle\left(-3,-\frac{3}{2}\right)$}](a) at (-3,-1.5){};
	\node[circle, inner sep=1pt, fill=white, draw=blue!50!black, label={above}:{$\scriptstyle\left(-1,\frac{1}{2}\right)$}](b) at (-1,.5){};
	\node[circle, inner sep=1pt, fill=white, draw=blue!50!black, label={above}:{$\scriptstyle\left(\frac{1}{2},2\right)$}](c) at (.5,2){};
	\node[circle, inner sep=1pt, fill=blue!50!black, draw=blue!50!black, label={right}:{$\scriptstyle\left(3,\frac{4}{7}\right)$}](d) at (3,{4/7}){};
	\begin{pgfonlayer}{bg}
	\draw[dashed, color=blue!50!black] (a) rectangle (0,0);
	\draw[dashed, color=blue!50!black] (b) rectangle (0,0);
	\draw[dashed, color=blue!50!black] (c) rectangle (0,0);
	\draw[dashed, color=blue!50!black] (d) rectangle (0,0);
	\end{pgfonlayer}
	\draw[orange,thick] (-3,0) -- (-1,0);
	\draw[orange,thick] (.5,0) -- (3,0);
	\end{tikzpicture}
\end{document}

Είναι συνεχής;

\documentclass[tikz, margin=5mm]{standalone}

\pgfdeclarelayer{bg}
\pgfsetlayers{bg,main}

\begin{document}
	\begin{tikzpicture}
	\draw[thick,->] (-4,0) -- (4,0)node[pos=1,below]{$x$};
	\draw[thick,->] (0,-2.7) -- (0,3)node[pos=1,left]{$y$};
	\begin{scope}
	\clip (-4,-2.7) rectangle (4,3);
	\draw[thick,blue!50!black, domain={.5}:{3},samples=100] plot (\x,{2/(\x+.5)});
	\draw[thick,blue!50!black, domain={-3}:{-1},samples=100] plot (\x,{1.5+\x});
	\end{scope}
	\node[circle, inner sep=1pt, fill=blue!50!black, draw=blue!50!black, label={left}:{$\scriptstyle\left(-3,-\frac{3}{2}\right)$}](a) at (-3,-1.5){};
	\node[circle, inner sep=1pt, fill=white, draw=blue!50!black, label={above}:{$\scriptstyle\left(-1,\frac{1}{2}\right)$}](b) at (-1,.5){};
	\node[circle, inner sep=1pt, fill=white, draw=blue!50!black, label={above}:{$\scriptstyle\left(\frac{1}{2},2\right)$}](c) at (.5,2){};
	\node[circle, inner sep=1pt, fill=blue!50!black, draw=blue!50!black, label={right}:{$\scriptstyle\left(3,\frac{4}{7}\right)$}](d) at (3,{4/7}){};
	\begin{pgfonlayer}{bg}
	\draw[dashed, color=blue!50!black] (a) rectangle (0,0);
	\draw[dashed, color=blue!50!black] (b) rectangle (0,0);
	\draw[dashed, color=blue!50!black] (c) rectangle (0,0);
	\draw[dashed, color=blue!50!black] (d) rectangle (0,0);
	\end{pgfonlayer}
	\end{tikzpicture}
\end{document}

Τι διαφορά έχει το πεδίο από το σύνολο τιμών;

\documentclass[tikz, margin=5mm]{standalone}

\usetikzlibrary{calc}

\begin{document}
	\begin{tikzpicture}
	\draw[thick] (0,0) ellipse (1.4 and 2.2)node[yshift=-2.4cm,xshift=-1cm]{$A$};
	\draw[thick] (6,0) ellipse (1.4 and 2.2)node[yshift=-2.4cm,xshift=1cm]{$B$};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={left}:{$a$}](a) at (.4,1.2){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={left}:{$b$}](b) at (-.2,.5){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={left}:{$c$}](c) at (.5,-.2){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={left}:{$d$}](d) at (-.6,-.9){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={left}:{$e$}](e) at (.3,-1.2){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={right}:{$1$}](1) at (6.3,1.3){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={right}:{$2$}](2) at (5.4,.6){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={right}:{$3$}](3) at (6.4,-.2){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={right}:{$4$}](4) at (6,-.8){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={right}:{$5$}](5) at (5.7,-1.5){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={right}:{$6$}](6) at (5.3,-.3){};
	\draw[thick,->] (a) -- (2);
	\draw[thick,->] (b) -- (6);
	\draw[thick,->] (c) -- (2);
	\draw[thick,->] (d) -- (5);
	\draw[thick,->] (e) -- (4);
	\node[draw=none](x) at ($(2)+(.1,.3)$){};
	\node[draw=none](y) at ($(4)+(.3,0)$){};
	\node[draw=none](z) at ($(5)+(0,-.3)$){};
	\node[draw=none](w) at ($(6)+(-.3,0)$){};
	\node[draw=none](m) at ($(6)+(.7,.2)$){};
	\draw[dashed, red, thick, fill=red, fill opacity=.1] plot [smooth cycle, tension=1] coordinates {(x.north east) (m) (y.north east) (z.south east) (w.west)};
	\node[label={above}:{$\textcolor{red}{f(A)}$}] at (x){};
	\end{tikzpicture}
\end{document}

Είναι η διπλανή σχέση συνάρτηση;

\documentclass[tikz, margin=5mm]{standalone}

\begin{document}
	\begin{tikzpicture}
	\draw[thick] (0,0) ellipse (1.4 and 2.2)node[yshift=-2.4cm,xshift=-1cm]{$A$};
	\draw[thick] (6,0) ellipse (1.4 and 2.2)node[yshift=-2.4cm,xshift=1cm]{$B$};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={left}:{$a$}](a) at (.4,1.2){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={left}:{$b$}](b) at (-.2,.5){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={left}:{$c$}](c) at (.5,-.2){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={left}:{$d$}](d) at (-.6,-.9){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={left}:{$e$}](e) at (.3,-1.2){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={right}:{$1$}](1) at (6.3,1.3){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={right}:{$2$}](2) at (5.4,.6){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={right}:{$3$}](3) at (6.4,-.2){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={right}:{$4$}](4) at (6,-.8){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={right}:{$5$}](5) at (5.7,-1.5){};
	\node[circle, inner sep=1pt, fill=black, draw=black, label={right}:{$6$}](6) at (5.3,-.3){};
	\draw[thick,->] (a) -- (2);
	\draw[thick,->] (a) -- (6);
	\draw[thick,->] (c) -- (2);
	\draw[thick,->] (d) -- (5);
	\draw[thick,->] (e) -- (4);
	\draw[thick,->] (d) -- (4);
	\end{tikzpicture}
\end{document}

Πολλοί λογάριθμοι…

\documentclass[tikz, margin=5mm]{standalone}

\begin{document}
	\begin{tikzpicture}
	\draw[thick,->] (-2,0) -- (6,0)node[pos=1,below]{$x$};
	\draw[thick,->] (0,-4) -- (0,4)node[pos=1,left]{$y$};
	\node[left,yshift=-8pt](O) at (0,0){$O$};
	\draw[thin,samples=200,domain={pow(exp(1),-3)}:{5}] plot (\x,{ln(\x)})node[right]{$y=\ln x$};
	\draw[dotted,samples=200,domain={pow(exp(1),-3)-1}:{5}] plot (\x,{ln(\x+1)})node[above]{$y=\ln(x+1)$};
	\draw[dashed,samples=200,domain={pow(exp(1),-3)-1}:{5}] plot (\x,{-ln(\x+1)})node[right]{$y=-\ln(x+1)$};
	\draw[very thick,samples=200,domain={pow(exp(1),-1)-1}:{5}] plot (\x,{2-ln(\x+1)})node[right,yshift=4pt]{$y=f(x)$};
	\end{tikzpicture}
\end{document}

Άλλη μία γνωστή γραφική παράσταση – πολύ γνωστή, ίσως…

\documentclass[tikz, margin=5mm]{standalone}

\begin{document}
	\begin{tikzpicture}
	\draw[thick,->] (-4,0) -- (4,0)node[below]{$x$};
	\draw[thick,->] (0,-4) -- (0,4)node[left]{$y$};
	\node[circle, inner sep=2pt, label={below,xshift=-5pt}:{$O$}] at (0,0){};
	\draw[thick, domain={-3}:{-.05}, samples=1000] plot ({\x},{.4*\x*\x*sin((8/(\x)) r)});
	\draw[thick, domain={.05}:{3}, samples=1000] plot ({\x},{.4*\x*\x*sin((8/(\x)) r)});
	\draw[domain={-3}:{3}, samples=200, dashed] plot ({\x},{.4*\x*\x});
	\draw[domain={-3}:{3}, samples=200, dashed] plot ({\x},{-.4*\x*\x});
	\node[circle, inner sep=1pt, fill=white, draw=black] at (0,0){};
	\end{tikzpicture}
\end{document}

Κι άλλη μία…

\documentclass[tikz, margin=5mm]{standalone}
\usepackage{xfrac}
\usetikzlibrary{calc}

\begin{document}
	\begin{tikzpicture}
	\draw[thick,->] (-1,0) -- (6,0)node[pos=1,below]{$x$};
	\draw[thick,->] (0,-1) -- (0,5)node[pos=1,left]{$y$};
	\node[circle, inner sep=1.5pt, draw=black, fill=black](o) at (0,0){};
	\begin{scope}
	\clip (-1,-1) rectangle (6,5);
	\draw[thick, domain={.001}:{7},samples=200] plot (\x,{\x*ln(\x)});
	\node[circle, inner sep=1.5pt, draw=black, fill=black](a) at ({1/exp(1)},{-1/exp(1)}){};
	\node[circle, inner sep=1.5pt, draw=black, fill=black, label={below}:{1}](b) at (1,0){};
	\draw[dashed] (o) rectangle (a);
	\node[left] at ($(0,-1)!(a)!(0,5)$){$-\sfrac{1}{e}$};
	\node[above] at ($(-1,0)!(a)!(5,0)$){$\sfrac{1}{e}$};
	\end{scope}
	\end{tikzpicture}
\end{document}

Άλλη μία γραφική παράσταση…

\documentclass[tikz, margin=5mm]{standalone}
\usepackage{xfrac}
\usetikzlibrary{calc}

\begin{document}
	\begin{tikzpicture}
	\draw[thick,->] (-1,0) -- (5,0)node[pos=1,below]{$x$};
	\draw[thick,->] (0,-5) -- (0,1)node[pos=1,left]{$y$};
	\draw[thick,domain={0}:{4},samples=100] plot (\x,{\x*\x*\x/3-2.5*\x*\x+4*\x-11/6});
	\node[circle, inner sep=1.5pt, draw=black, fill=black, label={left}:{$f(0)$}](a) at (0,{-11/6}){};
	\node[circle, inner sep=1.5pt, draw=black, fill=black, label={above}:{1}](b) at (1,0){};
	\node[circle, inner sep=1.5pt, draw=black, fill=black](d) at (2.5,{-27/12}){};
	\node[circle, inner sep=1.5pt, draw=black, fill=black](c) at (4,{-27/6}){};
	\node[above](e) at ($(0,0)!(c)!(4,0)$){$4$};
	\node[left](f) at ($(0,0)!(c)!(0,-3)$){$f(4)$};
	\draw[dashed] (0,0) rectangle (c);
	\draw[dashed] (0,0) rectangle (d);
	\node[left,yshift=-4pt] at ($(0,1)!(d)!(0,-5)$){$f(\sfrac{5}{2})$};
	\node[above] at ($(-1,0)!(d)!(5,0)$){$\sfrac{5}{2}$};
	\end{tikzpicture}
\end{document}

Ένα δέντρο…

\documentclass[tikz, margin=5mm]{standalone}
\usepackage{xfrac} % You know, only for the fancy inline fractions.

\begin{document}
	\begin{tikzpicture}
	\node[circle, minimum size=.9cm, draw=black](1) at (0,0){1};
	\node[circle, minimum size=.9cm, draw=black](2) at (2,0){2};
	\node[circle, minimum size=.9cm, draw=black](4) at (4,0){4};
	\node[circle, minimum size=.9cm, draw=black](8) at (6,0){8};
	\node[circle, minimum size=.9cm, draw=black](16) at (8,0){16};
	\node[circle, minimum size=.9cm, draw=black](32) at (10,0){32};
	\node[circle, minimum size=.9cm, draw=black](5) at (10,2){5};
	\node[circle, minimum size=.9cm, draw=black](10) at (12,2){10};
	\node[circle, minimum size=.9cm, draw=black](20) at (14,2){20};
	\node[circle, minimum size=.9cm, draw=black](3) at (14,4){3};
	\node[circle, minimum size=.9cm, draw=black](64) at (12,0){64};
	\node[circle, minimum size=.9cm, draw=black](128) at (14,0){128};
	\node[circle, minimum size=.8cm, draw=black](21) at (14,-2){21};
	\draw[thick, ->] (1) -- (2);
	\draw[thick, ->] (2) -- (4);
	\draw[thick, ->] (4) -- (8);
	\draw[thick, ->] (8) -- (16);
	\draw[thick, ->] (16) -- (32);
	\draw[thick, ->] (32) -- (64);
	\draw[thick, ->] (64) -- (128);
	\draw[thick, ->] (64) -- (21);
	\draw[thick, ->] (5) -- (10);
	\draw[thick, ->] (10) -- (20);
	\draw[thick, ->] (10) -- (3);
	\draw[thick, ->] (16) -- (5);
	\end{tikzpicture}
\end{document}

Μεγάλο χωρίο…

\documentclass[tikz, margin=5mm]{standalone}
\usepackage{xfrac}

\begin{document}
	\begin{tikzpicture}
	\draw[thick,->] (-1,0) -- (4,0)node[pos=1,below]{$x$};
	\draw[thick,->] (0,-2) -- (0,5)node[pos=1,left]{$y$};
	\draw[dashed] (0,0) rectangle (2,4);
	\begin{scope}
	\clip (-1,-2) rectangle (4,5);
	\draw[thick, domain={-1}:{4},samples=200] plot (\x,{\x*\x});
	\draw[thick, domain={1.1}:{4},samples=200] plot (\x,{4+4*ln(\x-1)});
	\draw[draw=none, fill=blue,fill opacity=0.1, smooth,samples=100,domain=0:2] plot(\x,{\x*\x}) -- (2,4) -- (1,0) -- (0,0) -- cycle;
	\draw[draw=none, fill=blue,fill opacity=0.1, smooth,samples=100,domain={1+exp(-1)}:2] plot(\x,{4+4*ln(\x-1)}) -- (2,4) -- (1,0) -- ({1+exp(-1)},0) -- cycle;
	\draw[thick,blue,domain={0}:{2},samples=200] plot(\x,{\x*\x});
	\draw[thick,blue,domain={(1+exp(-1))}:{2},samples=200] plot(\x,{4+4*ln(\x-1)});
	\draw[thick,blue] (0,0) -- ({1+exp(-1)},0);
	\node[below] at (2,0){2};
	\node[left] at (0,4){4};
	\node[below,xshift=-.7cm] at ({1+exp(-1)},0){$1+\sfrac{1}{e}$};
	\end{scope}
	\end{tikzpicture}
\end{document}

Αρχίσαμε τα χρωματιστά, ξανά…

\documentclass[tikz, margin=5mm]{standalone}

\begin{document}
	\begin{tikzpicture}
	\draw[thick,->] (-1,0) -- (7,0)node[pos=1,below]{$x$};
	\draw[thick,->] (0,-3) -- (0,5)node[pos=1,left]{$y$};
	\begin{scope}
	\clip (-1,-3) rectangle (7,5);
	\draw[thick, domain={exp(-3)}:{7},samples=200] plot (\x,{ln(\x)});
	\draw[thick, domain={-1}:{7}] plot (\x,{\x-1});
	\draw[thick, domain={-1}:{7}] plot (\x,{\x/6+ln(6)-1});
	\draw[draw=blue, fill=blue,fill opacity=0.1, smooth,samples=100,domain=1:6] plot(\x,{ln(\x)}) -- (6,{ln(6)}) -- ({(6*ln(6))/5},{(6*ln(6))/5-1}) -- (1,0) -- cycle;
	\draw[dashed] (0,0) rectangle (6,{ln(6)});
	\node[below] at (6,0){$\lambda$};
	\node[above,xshift=-.7cm] at ({(6*ln(6))/5},{(6*ln(6))/5-1}){$A(x_0,y_0)$};
	\node[left] at (0,{ln(6)}){$\ln\lambda$};
	\node[below] at (1,0){1};
	\end{scope}
	\end{tikzpicture}
\end{document}

Μάλλον είναι κι αυτό παραβολή…

\documentclass[tikz, margin=5mm]{standalone}
\usepackage{xfrac}
\usetikzlibrary{calc}

\begin{document}
	\begin{tikzpicture}
	\draw[thick,->] (-1,0) -- (6,0)node[pos=1,below]{$x$};
	\draw[thick,->] (0,-6) -- (0,2)node[pos=1,left]{$y$};
	\draw[thick, domain={0}:{5}, samples=50] plot (\x,{-.5*(\x-2)*(\x-5)});
	\node[circle, inner sep=1.5pt, draw=black, fill=black, label={below}:{5}](a) at (5,0){};
	\node[circle, inner sep=1.5pt, draw=black, fill=black, label={below}:{2}](b) at (2,0){};
	\node[circle, inner sep=1.5pt, draw=black, fill=black, label={left}:{-5}](c) at (0,-5){};
	\node[circle, inner sep=1.5pt, draw=black, fill=black](d) at (3.5,1.125){};
	\draw[dashed] (0,0) rectangle (d);
	\node[below] at ($(-1,0)!(d)!(6,0)$){$\sfrac{7}{2}$};
	\node[left] at ($(0,-5)!(d)!(0,1)$){$\sfrac{9}{8}$};
	\end{tikzpicture}
\end{document}

Απλό και καθημερινό…

\documentclass[tikz, margin=5mm]{standalone}
\usepackage{xfrac}

\usetikzlibrary{calc}

\begin{document}
	\begin{tikzpicture}
	\draw[thick,->] (-1,0) -- (5,0)node[pos=1,below]{$x$};
	\draw[thick,->] (0,-3) -- (0,5)node[pos=1,left]{$y$};
	\draw[thick,domain={0}:{4},samples=100] plot (\x,{(\x-1)*(\x-4)});
	\node[circle, inner sep=1.5pt, draw=black, fill=black, label={left}:{4}](a) at (0,4){};
	\node[circle, inner sep=1.5pt, draw=black, fill=black, label={above}:{1}](b) at (1,0){};
	\node[circle, inner sep=1.5pt, draw=black, fill=black, label={above}:{4}](d) at (4,0){};
	\node[circle, inner sep=1.5pt, draw=black, fill=black](c) at (2.5,-2.25){};
	\node[above](e) at ($(0,0)!(c)!(4,0)$){$\sfrac{5}{2}$};
	\node[left](f) at ($(0,0)!(c)!(0,-3)$){$-\sfrac{9}{4}$};
	\draw[dashed] (0,0) rectangle (c);
	\end{tikzpicture}
\end{document}

Ένα απλό συνημίτονο…

\documentclass[tikz, margin=5mm]{standalone}

\begin{document}
	\begin{tikzpicture}
	\draw[thick, ->] (-1,0) -- (7,0)node[pos=1,below]{$x$};
	\draw[thick, ->] (0,-2) -- (0,2)node[pos=1,left]{$y$};
	\draw[dashed] (-.99,-1.99) grid (6.99,1.99);
	\draw[thick, blue, samples=100, domain={0}:{pi}] plot (\x,{cos(\x r)});
	\draw[thick, red, samples=100, domain={pi}:{2*pi}] plot (\x,{cos(\x r)})node[right,yshift=8pt,black]{$y=\cos x$};
	\node[circle, draw=black, fill=black, inner sep=1.5pt, label={below,xshift=8pt}:{$\scriptstyle(\pi,-1)$}](a) at (pi,-1){};
	\end{tikzpicture}
\end{document}

Πώς προκύπτει η μπλε από την μαύρη καμπύλη;

\documentclass[tikz, margin=5mm]{standalone}

\begin{document}
	\begin{tikzpicture}
	\draw[dashed] (-3.99,-3.99) grid (3.99,3.99);
	\draw[thick, ->] (-4,0) -- (4,0)node[pos=1,below]{$x$};
	\draw[thick, ->] (0,-4) -- (0,4)node[pos=1,left]{$y$};
	\draw[thick, dashed, domain={-2}:{3}, samples=100] plot (\x,{0.25*(\x-1)*(\x+1)*(\x+1)*(\x-3)});
	\draw[thick, blue, domain={-3}:{2}, samples=100] plot (\x,{2-abs(0.25*\x*(\x+2)*(\x+2)*(\x-2))});
	\node[circle, inner sep=1.5pt, draw=black, fill=black, label={right,yshift=8pt}:{$(3,0)$}] at (3,0){};
	\node[circle, inner sep=1.5pt, draw=black, fill=black] at (-2,3.8){};
	\node[circle, inner sep=1.5pt, draw=blue, fill=blue, label={right,yshift=8pt}:{}] at (2,2){};
	\node[circle, inner sep=1.5pt, draw=blue, fill=blue] at (-3,-1.8){};
	\end{tikzpicture}
\end{document}

Μία λίγο πιο περίπλοκη αντανάκλαση…

\documentclass[tikz, margin=5mm]{standalone}

\begin{document}
	\begin{tikzpicture}
	\draw[dashed] (-3.99,-3.99) grid (3.99,3.99);
	\draw[thick, ->] (-4,0) -- (4,0)node[pos=1,below]{$x$};
	\draw[thick, ->] (0,-4) -- (0,4)node[pos=1,left]{$y$};
	\draw[thick, blue, domain={-3}:{3}, samples=100] plot (\x,{0.25*(abs(\x)-1)*(abs(\x)+1)*(abs(\x)+1)*(abs(\x)-3)});
	\draw[thick, dashed, domain={-2}:{3}, samples=100] plot (\x,{0.25*(\x-1)*(\x+1)*(\x+1)*(\x-3)});
	\node[circle, inner sep=1.5pt, draw=black, fill=black, label={right,yshift=8pt}:{$(3,0)$}] at (3,0){};
	\node[circle, inner sep=1.5pt, draw=black, fill=black] at (-2,3.8){};
	\node[circle, inner sep=1.5pt, draw=blue, fill=blue, label={right,yshift=8pt}:{}] at (3,0){};
	\node[circle, inner sep=1.5pt, draw=blue, fill=blue] at (-3,0){};
	\end{tikzpicture}
\end{document}

Και μία μεταφορά…

\documentclass[tikz, margin=5mm]{standalone}

\begin{document}
	\begin{tikzpicture}
	\draw[dashed] (-3.99,-3.99) grid (3.99,3.99);
	\draw[thick, ->] (-4,0) -- (4,0)node[pos=1,below]{$x$};
	\draw[thick, ->] (0,-4) -- (0,4)node[pos=1,left]{$y$};
	\draw[thick, dashed, domain={-2}:{3}, samples=100] plot (\x,{0.25*(\x-1)*(\x+1)*(\x+1)*(\x-3)});
	\draw[thick, blue, domain={-4}:{1}, samples=100] plot (\x,{0.25*(\x+1)*(\x+3)*(\x+3)*(\x-1)});
	\node[circle, inner sep=1.5pt, draw=black, fill=black, label={right,yshift=8pt}:{$(3,0)$}] at (3,0){};
	\node[circle, inner sep=1.5pt, draw=black, fill=black] at (-2,3.8){};
	\node[circle, inner sep=1.5pt, draw=blue, fill=blue, label={right,yshift=8pt}:{}] at (1,0){};
	\node[circle, inner sep=1.5pt, draw=blue, fill=blue] at (-4,3.8){};
	\end{tikzpicture}
\end{document}

Μία αντανάκλαση ακόμα…

\documentclass[tikz, margin=5mm]{standalone}

\begin{document}
	\begin{tikzpicture}
	\draw[dashed] (-3.99,-3.99) grid (3.99,3.99);
	\draw[thick, ->] (-4,0) -- (4,0)node[pos=1,below]{$x$};
	\draw[thick, ->] (0,-4) -- (0,4)node[pos=1,left]{$y$};
	\draw[thick, dashed, domain={-2}:{3}, samples=100] plot (\x,{0.25*(\x-1)*(\x+1)*(\x+1)*(\x-3)});
	\draw[thick, blue, domain={-3}:{2}, samples=100] plot (\x,{0.25*(-\x-1)*(-\x+1)*(-\x+1)*(-\x-3)});
	\node[circle, inner sep=1.5pt, draw=black, fill=black, label={right,yshift=8pt}:{$(3,0)$}] at (3,0){};
	\node[circle, inner sep=1.5pt, draw=black, fill=black] at (-2,3.8){};
	\node[circle, inner sep=1.5pt, draw=blue, fill=blue, label={right,yshift=8pt}:{}] at (-3,0){};
	\node[circle, inner sep=1.5pt, draw=blue, fill=blue] at (2,3.8){};
	\end{tikzpicture}
\end{document}

Απολύτως…

\documentclass[tikz, margin=5mm]{standalone}

\begin{document}
	\begin{tikzpicture}
	\draw[dashed] (-3.99,-3.99) grid (3.99,3.99);
	\draw[thick, ->] (-4,0) -- (4,0)node[pos=1,below]{$x$};
	\draw[thick, ->] (0,-4) -- (0,4)node[pos=1,left]{$y$};
	\draw[thick, blue, domain={-2}:{3}, samples=100] plot (\x,{abs(0.25*(\x-1)*(\x+1)*(\x+1)*(\x-3))});
	\draw[thick, dashed, domain={-2}:{3}, samples=100] plot (\x,{0.25*(\x-1)*(\x+1)*(\x+1)*(\x-3)});
	\node[circle, inner sep=1.5pt, draw=black, fill=black, label={right,yshift=8pt}:{$(3,0)$}] at (3,0){};
	\node[circle, inner sep=1.5pt, draw=black, fill=black] at (-2,3.8){};
	\node[circle, inner sep=1.5pt, draw=blue, fill=blue, label={right,yshift=8pt}:{}] at (3,0){};
	\node[circle, inner sep=1.5pt, draw=blue, fill=blue] at (-2,3.8){};
	\end{tikzpicture}
\end{document}

Αντανακλάσεις…

\documentclass[tikz, margin=5mm]{standalone}

\begin{document}
	\begin{tikzpicture}
	\draw[dashed] (-3.99,-3.99) grid (3.99,3.99);
	\draw[thick, ->] (-4,0) -- (4,0)node[pos=1,below]{$x$};
	\draw[thick, ->] (0,-4) -- (0,4)node[pos=1,left]{$y$};
	\draw[thick, dashed, domain={-2}:{3}, samples=100] plot (\x,{0.25*(\x-1)*(\x+1)*(\x+1)*(\x-3)});
	\draw[thick, blue, domain={-2}:{3}, samples=100] plot (\x,{-0.25*(\x-1)*(\x+1)*(\x+1)*(\x-3)});
	\node[circle, inner sep=1.5pt, draw=black, fill=black] at (-2,3.8){};
	\node[circle, inner sep=1.5pt, draw=blue, fill=blue, label={right,yshift=8pt,black}:{$(3,0)$}] at (3,0){};
	\node[circle, inner sep=1.5pt, draw=blue, fill=blue] at (-2,-3.8){};
	\end{tikzpicture}
\end{document}

Μία απλοποίηση του προηγούμενου σχήματος…

\documentclass[tikz, margin=5mm]{standalone}

\begin{document}
	\begin{tikzpicture}
	\draw[dashed] (-3.99,-3.99) grid (3.99,3.99);
	\draw[thick, ->] (-4,0) -- (4,0)node[pos=1,below]{$x$};
	\draw[thick, ->] (0,-4) -- (0,4)node[pos=1,left]{$y$};
	\draw[thick, dashed, domain={-2}:{3}, samples=100] plot (\x,{0.25*(\x-1)*(\x+1)*(\x+1)*(\x-3)});
	\draw[thick, blue, domain={-2}:{3}, samples=100] plot (\x,{0.25*(\x-1)*(\x+1)*(\x+1)*(\x-3)-1});
	\node[circle, inner sep=1.5pt, draw=black, fill=black, label={right,yshift=8pt}:{$(3,0)$}] at (3,0){};
	\node[circle, inner sep=1.5pt, draw=black, fill=black] at (-2,3.8){};
	\node[circle, inner sep=1.5pt, draw=blue, fill=blue, label={right,yshift=8pt}:{}] at (3,-1){};
	\node[circle, inner sep=1.5pt, draw=blue, fill=blue] at (-2,2.8){};
	\end{tikzpicture}
\end{document}

Ωραίο πράσινο χωρίο αυτό…

\documentclass[tikz, margin=5mm]{standalone}

\begin{document}
	\begin{tikzpicture}
	\begin{scope}
	\clip (-4,-4) rectangle (4,4);
	\draw[thick, dashed, fill=green!40!black, fill opacity=.4, domain={-2}:{3}, samples=100] plot (\x,{0.25*(\x-1)*(\x+1)*(\x+1)*(\x-3)+1}) -- plot ((1-\x,{0.25*(1-\x-1)*(1-\x+1)*(1-\x+1)*(1-\x-3)-1}) -- (-2,4) -- cycle;
	\end{scope}
	\draw[dashed] (-3.99,-3.99) grid (3.99,3.99);
	\draw[thick, ->] (-4,0) -- (4,0)node[pos=1,below]{$x$};
	\draw[thick, ->] (0,-4) -- (0,4)node[pos=1,left]{$y$};
	\draw[thick, domain={-2}:{3}, samples=100] plot (\x,{0.25*(\x-1)*(\x+1)*(\x+1)*(\x-3)});
	\node[circle, inner sep=1.5pt, draw=black, fill=black, label={right,yshift=8pt}:{$(3,0)$}] at (3,0){};
	\node[circle, inner sep=1.5pt, draw=black, fill=black] at (-2,3.8){};
	\end{tikzpicture}
\end{document}

Μία κοινή εφαπτομένη…

\documentclass[tikz, margin=5mm]{standalone}

\begin{document}
	\begin{tikzpicture}
	\draw[dashed] (-3.99,-3.99) grid (3.99,3.99);
	\draw[thick,->] (-4,0) -- (4,0)node[pos=1,below]{$x$};
	\draw[thick,->] (0,-4) -- (0,4)node[pos=1,left]{$y$};
	\begin{scope}
	\clip (-4,-4) rectangle (4,4);
	\draw[thick, purple, samples=200] plot (\x,{\x*\x-2*\x+1});
	\draw[thick, orange, samples=200] plot (\x,{-2*\x+1});
	\draw[thick, blue, samples=200] plot (\x,{-2*\x*\x-2*\x+1});
	\end{scope}
	\node[purple, above] at (3,4){$a=1$};
	\node[orange, above] at (-1.5,4){$a=0$};
	\node[blue, below] at (1,-4){$a=-2$};
	\end{tikzpicture}
\end{document}

Ευθείες παντού!

\documentclass[tikz, margin=5mm]{standalone}
\usepackage{xfrac}

\begin{document}
	\begin{tikzpicture}
	\draw[dashed] (-3.99,-3.99) grid (3.99,3.99);
	\draw[thick,->] (-4,0) -- (4,0)node[pos=1,below]{$x$};
	\draw[thick,->] (0,-4) -- (0,4)node[pos=1,left]{$y$};
	\begin{scope}
	\clip (-4,-4) rectangle (4,4);
	\draw[thick, purple] plot (\x,{0});
	\draw[thick, orange] plot (\x,{\x});
	\draw[thick, blue] plot (\x,{0.5*\x});
	\draw[thick, red] plot (\x,{-\x});
	\end{scope}
	\node[purple, right] at (4,0){$f_0$};
	\node[orange, above] at (4,4){$f_1$};
	\node[red, right] at (4,-4){$f_{-1}$};
	\node[blue, right] at (4,2){$f_{\sfrac{1}{2}}$};
	\end{tikzpicture}
\end{document}

Μάλλον είναι πολλές οι καμπύλες…

\documentclass[tikz, margin=5mm]{standalone}

\begin{document}
	\begin{tikzpicture}
	\draw[dashed] (-3.99,-3.99) grid (3.99,3.99);
	\draw[thick,->] (-4,0) -- (4,0)node[pos=1,below]{$x$};
	\draw[thick,->] (0,-4) -- (0,4)node[pos=1,left]{$y$};
	\begin{scope}
	\clip (-4,-4) rectangle (4,4);
	\draw[thick, dashed, opacity=.8, purple, samples=50, domain={0.01}:{4}] plot (\x,{1/\x});
	\draw[thick, dashed, opacity=.8, purple, samples=50, domain={-4}:{-0.01}] plot (\x,{1/\x});
	\draw[thick, dashed, opacity=.8, orange, samples=50, domain={1.01}:{4}] plot (\x,{1/(\x-1)});
	\draw[thick, dashed, opacity=.8, orange, samples=50, domain={-4}:{0.99}] plot (\x,{1/(\x-1)});
	\draw[thick, blue, samples=50, domain={1.01}:{4}] plot (\x,{1/abs((abs(\x)-1))});
	\draw[thick, blue, samples=50, domain={-4}:{-1.01}] plot (\x,{1/abs((abs(\x)-1))});
	\draw[thick, blue, samples=50, domain={-0.99}:{0.99}] plot (\x,{1/abs((abs(\x)-1))});
	\draw[thick, dashed, opacity=.9, red, samples=50, domain={1.01}:{4}] plot (\x,{1/(abs(\x)-1)});
	\draw[thick, dashed, opacity=.9, red, samples=50, domain={-4}:{-1.01}] plot (\x,{1/(abs(\x)-1)});
	\draw[thick, dashed, opacity=.9, red, samples=50, domain={-0.99}:{0.99}] plot (\x,{1/(abs(\x)-1)});
	\end{scope}
	\node[purple, opacity=.9, right] at (4,.2){$\frac{1}{x}$};
	\node[orange, opacity=.9, above] at (1,4){$\frac{1}{x-1}$};
	\node[red, opacity=.9, left] at (-4,.2){$\frac{1}{|x|-1}$};
	\node[blue, above] at (-1,4){$f$};
	\end{tikzpicture}
\end{document}

Γιατί έπαψες λογάριθμο να θυμίζεις;

\documentclass[tikz, margin=5mm]{standalone}

\begin{document}
	\begin{tikzpicture}
	\draw[dashed] (-3.99,-3.99) grid (3.99,3.99);
	\draw[thick,->] (-4,0) -- (4,0)node[pos=1,below]{$x$};
	\draw[thick,->] (0,-4) -- (0,4)node[pos=1,left]{$y$};
	\begin{scope}
	\clip (-4,-4) rectangle (4,4);
	\draw[thick, dashed, opacity=.8, purple, samples=50, domain={0.01}:{4}] plot (\x,{ln(\x)});
	\draw[thick, dashed, opacity=.8, orange, samples=50, domain={-4}:{-0.01}] plot (\x,{ln(-\x)});
	\draw[thick, dashed, opacity=.8, brown, samples=50, domain={-4}:{1.99}] plot (\x,{ln(2-\x)});
	\draw[thick, densely dotted, opacity=.8, green!40!black, samples=50, domain={-1.99}:{1.99}] plot (\x,{ln(2-abs(\x))});
	\draw[thick, dashed, opacity=.8, red, samples=50, domain={-1.99}:{1.99}] plot (\x,{-ln(2-abs(\x))});
	\draw[thick, blue, samples=50, domain={-1.99}:{1.99}] plot (\x,{1-ln(2-abs(\x))});
	\end{scope}
	\node[purple, opacity=.9, right] at (4,1.4){$\ln x$};
	\node[orange, opacity=.9, left] at (-4,1.4){$\ln(-x)$};
	\node[brown, opacity=.9, left] at (-4,1.9){$\ln(2-x)$};
	\node[green!40!black, opacity=.9, below] at (-2,-4){$\ln(2-|x|)$};
	\node[red, opacity=.9, above] at (2,4){$-\ln(2-|x|)$};
	\node[blue, above] at (-2,4){$f$};
	\end{tikzpicture}
\end{document}

Πολύ χρώμα, ρε παιδί μου…

\documentclass[tikz, margin=5mm]{standalone}

\begin{document}
	\begin{tikzpicture}
	\draw[dashed] (-3.99,-3.99) grid (3.99,3.99);
	\draw[thick,->] (-4,0) -- (4,0)node[pos=1,below]{$x$};
	\draw[thick,->] (0,-4) -- (0,4)node[pos=1,left]{$y$};
	\begin{scope}
	\clip (-4,-4) rectangle (4,4);
	\draw[thick, thick, blue, samples=200] plot (\x,{1+abs(1-exp(-\x))});
	\draw[thick, dashed, opacity=.8, purple, samples=50] plot (\x,{exp(\x)});
	\draw[thick, dashed, opacity=.8, orange, samples=50] plot (\x,{exp(-\x)});
	\draw[thick, dashed, opacity=.8, brown, samples=50] plot (\x,{-exp(-\x)});
	\draw[thick, dashed, opacity=.8, green!40!black, samples=50] plot (\x,{1-exp(-\x)});
	\draw[thick, densely dotted, opacity=.8, red, samples=50] plot (\x,{abs(1-exp(-\x))});
	\end{scope}
	\node[purple, opacity=.9, right] at (1.4,4){$e^x$};
	\node[orange, opacity=.9, above] at (-1.3,4){$e^{-x}$};
	\node[brown, opacity=.9, left, yshift=-4pt] at (-1.3,-4){$-e^{-x}$};
	\node[green!40!black, opacity=.9, right] at (4,1){$1-e^{-x}$};
	\node[red, opacity=.9, left] at (-1.5,4){$\left|1-e^{-x}\right|$};
	\node[blue, right] at (4,2){$f$};
	\end{tikzpicture}
\end{document}

Μία κυβική καμπύλη – αλήθεια, ποιος είναι ο τύπος της;

\documentclass[tikz, margin=5mm]{standalone}

\begin{document}
	\begin{tikzpicture}
	\draw[dashed] (-3.99,-3.99) grid (3.99,3.99);
	\draw[thick,->] (-4,0) -- (4,0)node[pos=1,below]{$x$};
	\draw[thick,->] (0,-4) -- (0,4)node[pos=1,left]{$y$};
	\begin{scope}
	\clip (-4,-4) rectangle (4,4);
	\draw[thick, dashed, opacity=.8, purple, samples=50] plot (\x,{\x*\x*\x});
	\draw[thick, dashed, opacity=.8, orange, samples=50] plot (\x,{-\x*\x*\x});
	\draw[thick, blue, samples=200] plot (\x,{2-\x*\x*\x});
	\end{scope}
	\node[purple, opacity=.9, right] at (1.5,4){$x^3$};
	\node[orange, opacity=.9, right, yshift=-2pt] at (1.5,-4){$-x^3$};
	\node[blue, right] at (-1.3,4){$f$};
	\end{tikzpicture}
\end{document}

Μία ακόμα τσαχπινιά σε ένα προηγούμενο σχήμα + χρώματα…

\documentclass[tikz, margin=5mm]{standalone}

\begin{document}
	\begin{tikzpicture}
	\fill[red!10] (-5,5) -- (6,5) -- (6,-5) -- (5,-5) -- cycle;
	\draw[dashed] (-5.99,-4.99) grid (5.99,4.99);
	\draw[thick, ->] (-6,0) -- (6,0)node[pos=1,below]{$x$};
	\draw[thick, ->] (0,-5) -- (0,5)node[pos=1,left]{$y$};
	\draw[thick, domain={-5}:{5}, samples=100] plot (\x,{0.025*(\x-1)*(\x+5)*(\x+2.5)*(\x-4.6)});
	\begin{scope}
	\clip (-5,5) -- (6,5) -- (6,-5) -- (5,-5) -- cycle;
	\draw[thick, red, domain={-5}:{5}, samples=100] plot (\x,{0.025*(\x-1)*(\x+5)*(\x+2.5)*(\x-4.6)});
	\end{scope}
	\node[circle, draw=black, inner sep=1.5pt, fill=white](a) at (-5,0){};
	\node[circle, draw=black, inner sep=1.5pt, fill=white, label={right,yshift=8pt}:{$(5,3)$}](b) at (5,3){};
	\draw[thick, domain={-5}:{5}, samples=100] plot (\x,{-\x})node[below]{$y=-x$};
	\draw[densely dotted] (-1.42,0) -- (-1.42,1.42);
	\draw[densely dotted] (3.5,0) -- (3.5,-3.5);
	\draw[very thick, blue] (3.5,0) -- (5,0);
	\draw[very thick, blue] (-1.42,0) -- (2,0);
	\end{tikzpicture}
\end{document}

Μία τσαχπινιά σε ένα προηγούμενο σχήμα + χρώματα…

\documentclass[tikz, margin=5mm]{standalone}

\begin{document}
	\begin{tikzpicture}
	\fill[red!10] (-6,-2) rectangle (6,-5);
	\fill[red!10] (-6,1) rectangle (6,5);
	\draw[dashed] (-5.99,-4.99) grid (5.99,4.99);
	\draw[thick, ->] (-6,0) -- (6,0)node[pos=1,below]{$x$};
	\draw[thick, ->] (0,-5) -- (0,5)node[pos=1,left]{$y$};
	\begin{scope}
	\clip (-6,1) rectangle (6,5);
	\draw[thick, red, domain={-5}:{5}, samples=100] plot (\x,{0.025*(\x-1)*(\x+5)*(\x+2.5)*(\x-4.6)});
	\end{scope}
	\begin{scope}
	\clip (-6,-2) rectangle (6,-5);
	\draw[thick, red, domain={-5}:{5}, samples=100] plot (\x,{0.025*(\x-1)*(\x+5)*(\x+2.5)*(\x-4.6)});
	\end{scope}
	\begin{scope}
	\clip (-6,-2) rectangle (6,1);
	\draw[thick, dashed, blue, domain={-5}:{5}, samples=100] plot (\x,{0.025*(\x-1)*(\x+5)*(\x+2.5)*(\x-4.6)});
	\end{scope}
	\node[circle, draw=black, inner sep=1.5pt, fill=white](a) at (-5,0){};
	\node[circle, draw=black, inner sep=1.5pt, fill=white, label={right,yshift=8pt}:{$(5,3)$}](b) at (5,3){};
	\draw[thick] (-6,1) -- (6,1)node[pos=1,right]{$y=1$};
	\draw[thick] (-6,-2) -- (6,-2)node[pos=1,right]{$y=-2$};
	\draw[densely dotted] (-1.8,0) rectangle (.4,1);
	\draw[densely dotted] (4.2,-2) -- (4.2,0);
	\draw[densely dotted] (4.75,1) -- (4.75,0);
	\draw[thick, red] (-1.8,0) -- (.4,0);
	\draw[thick, red] (2,0) -- (4.2,0);
	\draw[thick, red] (4.75,0) -- (5,0);
	\end{tikzpicture}
\end{document}

Μία τσαχπινιά σε ένα προηγούμενο σχήμα…

\documentclass[tikz, margin=5mm]{standalone}

\begin{document}
	\begin{tikzpicture}
	\draw[thick, ->] (-6,0) -- (6,0)node[pos=1,below]{$x$};
	\draw[thick, ->] (0,-5) -- (0,5)node[pos=1,left]{$y$};
	\draw[thick, domain={-5}:{-2.5}, samples=100] plot (\x,{0.025*(\x-1)*(\x+5)*(\x+2.5)*(\x-4.6)});
	\draw[thick, domain={1}:{5}, samples=100] plot (\x,{0.025*(\x-1)*(\x+5)*(\x+2.5)*(\x-4.6)});
	\draw[thick, dashed, domain={-2.5}:{1}, samples=100] plot (\x,{0.025*(\x-1)*(\x+5)*(\x+2.5)*(\x-4.6)});
	\node[circle, draw=black, inner sep=1.5pt, fill=white](a) at (-5,0){};
	\node[circle, draw=black, inner sep=1.5pt, fill=white, label={right,yshift=8pt}:{$(5,3)$}](b) at (5,3){};
	\draw[thick, domain={-2.5}:{2.5}, samples=100] plot (\x,{2*\x})node[above]{$y=ax$};
	\end{tikzpicture}
\end{document}

Η γραφική παράσταση ενός πολυωνύμου με λίγη παρέα…

\documentclass[tikz, margin=5mm]{standalone}

\begin{document}
	\begin{tikzpicture}
	\draw[dashed] (-5.99,-4.99) grid (5.99,4.99);
	\draw[thick, ->] (-6,0) -- (6,0)node[pos=1,below]{$x$};
	\draw[thick, ->] (0,-5) -- (0,5)node[pos=1,left]{$y$};
	\draw[thick, domain={-5}:{5}, samples=100] plot (\x,{0.025*(\x-1)*(\x+5)*(\x+2.5)*(\x-4.6)});
	\node[circle, draw=black, inner sep=1.5pt, fill=white](a) at (-5,0){};
	\node[circle, draw=black, inner sep=1.5pt, fill=white, label={right,yshift=8pt}:{$(5,3)$}](b) at (5,3){};
	\draw[thick, domain={-1.7}:{1.7}, samples=100] plot (\x,{\x*\x*\x})node[above]{$y=x^3$};
	\end{tikzpicture}
\end{document}

Η γραφική παράσταση ενός πολυωνύμου…

\documentclass[tikz, margin=5mm]{standalone}
\usepackage{xfrac} % You know, only for the fancy inline fractions.

\begin{document}
	\begin{tikzpicture}
	\draw[thick,->] (-.5,0) -- (7,0)node[pos=1,below]{$x$};
	\draw[thick,->] (0,-1.5) -- (0,5)node[pos=1,left]{$y$};
	\draw[thick, domain={0}:{6}, samples=100] plot (\x,{(3/75)*(\x^2-1)*(\x-3)*(\x-5)*(\x-5)});
	\draw[dashed] (-.49,-1.49) grid (6.99,4.99);
	\node[circle, inner sep=1.5pt, draw=black, fill=white, label={left,yshift=10pt}:{$A(0,3)$}](a) at (0,3){};
	\node[circle, inner sep=1.5pt, draw=black, fill=white, label={right}:{$B(6,\sfrac{17}{4})$}](a) at (6,4.25){};
	\end{tikzpicture}
\end{document}

Η γνωστή μας και μη εξαιρετέα καμπάνα της κανονικής κατανομής!

\documentclass[tikz, margin=5mm]{standalone}
\usepackage{ifthen} % In order to use the ifthenelse structure.

\begin{document}
	\begin{tikzpicture}
	\draw[thick, ->] (-4,0) -- (4,0);
	\draw[thick, ->] (0,-.1) -- (0,3)node[pos=0,below]{$\mu$};
	\draw[dashed] (-3.99,0) grid (3.99,2.99);
	\draw[thick, domain={-3.9}:{3.9}, samples=200, draw=blue] plot (\x,{2.6*exp(-\x*\x/2)});
	\foreach \i in {-3,-2,-1,1,2,3}{
		\ifthenelse{\i>0}{
			\draw (\i,-.1) -- (\i,.1)node[pos=0,below]{$+\i\sigma$};
		}{
			\draw (\i,-.1) -- (\i,.1)node[pos=0,below]{$\i\sigma$};
		}
	}
	\draw[thick, <->] (-1,-.7) -- (1,-.7)node[pos=.5,below]{$68.2\%$};
	\draw[thick, <->] (-2,-1.4) -- (2,-1.4)node[pos=.5,below]{$95.4\%$};
	\draw[thick, <->] (-3,-2.1) -- (3,-2.1)node[pos=.5,below]{$99.8\%$};
	\draw[densely dotted] (-2,-1.4) -- (-2,-.7);
	\draw[densely dotted] (2,-1.4) -- (2,-.7);
	\draw[densely dotted] (-3,-2.1) -- (-3,-.7);
	\draw[densely dotted] (3,-2.1) -- (3,-.7);
	\end{tikzpicture}
\end{document}

Μία απλή απόδειξη ότι το [0,1] και το (0,1) είναι ισοπληθικά…

\documentclass[tikz, margin=5mm]{standalone}
\usepackage{xfrac} % Used to load to \sfrac command which typesets nice inline fractions.

\begin{document}
	\begin{tikzpicture}
	\draw[thick] (-1,0) -- (8,0);
	\draw[thick] (-1,-2) -- (8,-2);
	\node[circle, inner sep=1pt, draw=black, fill=black, label={above}:{0}](a0) at (0,0){};
	\node[circle, inner sep=1pt, draw=black, fill=black, label={above}:{1}](a1) at (1,0){};
	\node[circle, inner sep=1pt, draw=black, fill=black, label={above}:{$\sfrac{1}{2}$}](a2) at (2,0){};
	\node[circle, inner sep=1pt, draw=black, fill=black, label={above}:{$\sfrac{1}{3}$}](a3) at (3,0){};
	\node[circle, inner sep=1pt, draw=black, fill=black, label={above}:{$\sfrac{1}{4}$}](a4) at (4,0){};
	\node[circle, inner sep=1pt, draw=black, fill=black, label={above}:{$\sfrac{1}{5}$}](a5) at (5,0){};
	\node[circle, inner sep=1pt, draw=black, fill=black, label={above}:{$\sfrac{1}{6}$}](a6) at (6,0){};
	\node[circle, inner sep=1pt, draw=black, fill=black, label={above}:{$\sfrac{1}{7}$}](a7) at (7,0){};
	\node[circle, inner sep=1pt, draw=black, fill=black, label={below}:{0}](b0) at (0,-2){};
	\node[circle, inner sep=1pt, draw=black, fill=black, label={below}:{1}](b1) at (1,-2){};
	\node[circle, inner sep=1pt, draw=black, fill=black, label={below}:{$\sfrac{1}{2}$}](b2) at (2,-2){};
	\node[circle, inner sep=1pt, draw=black, fill=black, label={below}:{$\sfrac{1}{3}$}](b3) at (3,-2){};
	\node[circle, inner sep=1pt, draw=black, fill=black, label={below}:{$\sfrac{1}{4}$}](b4) at (4,-2){};
	\node[circle, inner sep=1pt, draw=black, fill=black, label={below}:{$\sfrac{1}{5}$}](b5) at (5,-2){};
	\node[circle, inner sep=1pt, draw=black, fill=black, label={below}:{$\sfrac{1}{6}$}](b6) at (6,-2){};
	\node[circle, inner sep=1pt, draw=black, fill=black, label={below}:{$\sfrac{1}{7}$}](b7) at (7,-2){};
	\draw[thick,->] (a0) -- (b2);
	\draw[thick,->] (a1) -- (b3);
	\draw[thick,->] (a2) -- (b4);
	\draw[thick,->] (a3) -- (b5);
	\draw[thick,->] (a4) -- (b6);
	\draw[thick,->] (a5) -- (b7);
	\end{tikzpicture}
\end{document}

Μία κομψή και ασυνεχής συνάρτηση – εντάξει, ίσως όχι τόσο κομψή…

\documentclass[tikz, margin=5mm]{standalone}
\usepackage{xfrac} % Used to load to \sfrac command which typesets nice inline fractions.

\begin{document}
	\begin{tikzpicture}
	\draw[dashed, step=3] (-0.49,-0.49) grid (3.99,3.99);
	\draw[thick, ->] (-.5,0) -- (4,0)node[pos=1,below]{$x$};
	\draw[thick, ->] (0,-.5) -- (0,4)node[pos=1,left]{$y$};
	\draw[thick, domain={0}:{3}, samples=100] plot (\x,{\x});
	%				\draw[thick, domain={0}:{3}, samples=100] plot (\x,{\x});
	\node[circle, draw=black, inner sep=1.5pt, fill=white, label={right,yshift=8pt}:{(1,1)}](a) at (3,3){};
	\node[circle, draw=black, inner sep=1.5pt, fill=white, label={left,yshift=-8pt}:{(0,0)}](b) at (0,0){};
	\node[circle, draw=black, inner sep=1.5pt, fill=black, label={left}:{$(0,\sfrac{1}{2})$}](c) at (0,1.5){};
	\node[circle, draw=black, inner sep=1.5pt, fill=black, label={right}:{$(1,\sfrac{1}{2})$}](d) at (3,1.5){};
	\end{tikzpicture}
\end{document}

Μία απλή γραφική παράσταση μίας «σχεδόν» γραμμικής συνάρτησης…

\documentclass[tikz, margin=5mm]{standalone}

\begin{document}
	\begin{tikzpicture}
	\draw[dashed] (-2.99,-2.99) grid (2.99,2.99);
	\draw[thick, ->] (-3,0) -- (3,0)node[pos=1,below]{$x$};
	\draw[thick, ->] (0,-3) -- (0,3)node[pos=1,left]{$y$};
	\draw[thick, domain={-3}:{0}, samples=100] plot (\x,{\x+1});
	\draw[thick, domain={0}:{3}, samples=100] plot (\x,{\x});
	\node[circle, draw=black, inner sep=1.5pt, fill=white](a) at (0,1){};
	\node[circle, draw=black, inner sep=1.5pt, fill=black](b) at (0,0){};
	\end{tikzpicture}
\end{document}