Grafici con Tikz numero 14 (funzioni)

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Prima di ogni figura ricordare di mettere

\documentclass[usenames,dvipsnames]{article}
\usepackage{pgfplots}

Figura 1

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codice prima figura

\begin{tikzpicture}
\begin{axis}[
axis x line=center,
axis y line=center,
xmin = -0.95,
xmax = 5.95,
ymin = -2.5,
ymax = 2.95,
xlabel = {$x$},
ylabel = {$y$},
extra x ticks = {0},
extra x tick label = {$\hspace{-0.6cm}O$},
]

\addplot[very thick, domain=0:6, samples=100,MidnightBlue,name path=radice] {sqrt(x)};
\addplot[very thick, samples=10,MidnightBlue,name path=retta] {x-2};
\addplot[very thick, samples=10,name path=asse,domain=0:4] {0};
\addplot[Orchid!30] fill between [of=asse and radice, soft clip={domain=0:2}];
\addplot[Orchid!30] fill between [of=retta and radice, soft clip={domain=2:4}];
\addplot[Dandelion!30] fill between [of=asse and retta, soft clip={domain=2:4}];

\addplot[mark=*,draw=none] coordinates {(0,0) (4,0) (4,2)} node[above left] {$C$};
\addplot[mark=*,draw=none] coordinates {(2,0)} node[above left] {$A$};
\addplot[very thick,dashed,no marks] coordinates {(4,2) (4,0)} node[above right] {$B$};

\addplot[MidnightBlue] coordinates {(0.9,-1.15)} node[below,rotate=45] {$y=x-2$};
\addplot[MidnightBlue] coordinates {(2,1.5)} node[above,rotate=18] {$y=\sqrt{x}$};
\end{axis}
\end{tikzpicture}

seconda figura

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codice seconda figura

\begin{tikzpicture}
\begin{axis}[
scale=1,
axis equal image,
axis x line=center,
axis y line=center,
xmin = -3.5,
xmax = 3.95,
ymin = -3.5,
ymax = 3.95,
xlabel = {$x$},
ylabel = {$y$},
extra x ticks = {0},
extra x tick label = {$\hspace{0.5cm}O$},
cycle list name=color list,
xtick={-3,-2,-1,1,2,3},
ytick={-3,-2,-1,1,2,3},
xticklabel style = {xshift={0.5ex}, yshift={0.5ex}, font=\tiny},
yticklabel style = {xshift={0.5ex}, yshift={0.75ex}, font=\tiny}
]

\foreach \x in {-3,-2,...,3} {
\foreach \y in {-3,-2,...,3} {
\addplot+[mark=*] coordinates {(\x,\y)};
};};
\addplot[ultra thick, domain=-2:2, samples=100,MidnightBlue] {sqrt(4-x^2)};
\addplot[ultra thick, domain=-2:2, samples=100,MidnightBlue] {-sqrt(4-x^2)};
\addplot[ultra thick, domain=-sqrt(5):sqrt(5), samples=100,MidnightBlue,dashed] {sqrt(5-x^2)};
\addplot[ultra thick, domain=-sqrt(5):sqrt(5), samples=100,MidnightBlue,dashed] {-sqrt(5-x^2)};
\addplot[thick,black,dotted] coordinates {(0,2) (1,2) (1,0)};
\addplot[thick,black,dotted] coordinates {(0,0) (1,2)};
\end{axis}
\end{tikzpicture}

terza figura

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codice terza figura

\begin{tikzpicture}
\begin{axis}[
axis on top,
width=\textwidth,
height=0.6\textwidth,
axis x line=center,
axis y line=center,
xmin = -4.9,
xmax = 4.9,
ymin = -2.9,
ymax = 2.9,
xlabel = {$x$},
ylabel = {$y$},
extra x ticks = {0},
extra x tick label = {$\hspace{-0.6cm}O$},
]

\addplot[very thick,OrangeRed,samples=100] {x^2-2};
\addplot[very thick,Orange,samples=100] {x^2-1};
\addplot[very thick,YellowOrange,samples=100] {x^2};
\addplot[very thick,Dandelion,samples=100] {x^2+3/4^(4/3)};
\addplot[very thick,Goldenrod,samples=100] {x^2+1};
\addplot[very thick,yellow,samples=100] {x^2+2};
\addplot[very thick,domain=0:4,samples=200,NavyBlue] {sqrt(x)};
\addplot[very thick,domain=0:4,samples=200,NavyBlue] {-sqrt(x)};

\addplot[mark=diamond*,only marks,OrangeRed,mark size=2pt] coordinates {(1,-1) (1.831,1.353)};
\addplot[mark=diamond*,only marks,Orange,mark size=2pt] coordinates {(0.525,-0.724) (1.49,1.221)};
\addplot[mark=diamond*,only marks,YellowOrange,mark size=2pt] coordinates {(0,0) (1,1)};

\addplot[mark=*,Orchid,mark size=2pt] coordinates {(0.3968,0.6299)};
\addplot[NavyBlue,no marks] coordinates {(2,-1.4142)} node[rotate=-15,below] {$x^2=y$};
\addplot[OrangeRed,no marks] coordinates {(-2,1.5)} node[rotate=-68,below] {$y=x^2+c$};
\addplot[no marks] coordinates {(-1,-2)} node[left] {$\scriptsize c = {\color{OrangeRed}-2},\ {\color{Orange} -1},\ {\color{YellowOrange} 0},\ {\color{Dandelion} \dfrac{3}{4\sqrt[3\,]{4}}},\ {\color{Goldenrod} 1},\ \color{yellow} 2$};
\end{axis}
\end{tikzpicture}

quarta figura

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codice quarta figura

\begin{tikzpicture}
\begin{axis}[
scale=0.8,
disabledatascaling,
axis equal image,
axis x line=none,
axis y line=none,
xmin = -1.2,
xmax = 1.2,
ymin = -1.2,
ymax = 1.2,
]

\draw[very thick,color=Blue] (axis cs:0,0) circle [radius=1];

\addplot[mark=*,very thick,BurntOrange] coordinates {(-0.707,0.707) (-0.5,-0.866) (1,0)};
\addplot[mark=*,very thick,Orchid] coordinates {(-0.707,0.707) (0,1) (1,0)};
\addplot[mark=*,very thick] coordinates {(-0.707,0.707) (1,0)};
\addplot[no marks,BurntOrange] coordinates {(-0.1,-0.1)} node {$T$};
\addplot[no marks,Orchid] coordinates {(0.05,0.65)} node {$S$};
\end{axis}
\end{tikzpicture}