Di seguito le immagini delle figure.

 

Codice prima figura

 

\begin{tikzpicture}
\begin{axis}[
axis x line=center,
axis y line=center,
xmin = -5,
xmax = 5.5,
ymin = -5,
ymax = 5.5,
xlabel = {$x$},
ylabel = {$y$},
extra x ticks = {0},
extra x tick label = {$\hspace{-0.9cm}0$},
y label style={anchor=north east}
]

\addplot[very thick,domain=-4:4,samples=100,name path=a] {sqrt(x^2+1)};
\addplot[very thick,domain=-4:4,samples=100,name path=b] {-sqrt(x^2+1)};
\addplot[thin, samples=10,name path=asse,domain=-4:4] {0};
\draw (0,-1) -- (0,1);
\addplot[black] coordinates {(2,3.7)} node[below,rotate=35] {$y=\sqrt{x^2+1}$};
\addplot[black] coordinates {(2.5,-2.7)} node[below,rotate=320] {$y=-\sqrt{x^2+1}$};

\addplot[tau] fill between [of=b and a, soft clip={domain=-4:4}];
\end{axis}
\end{tikzpicture}

 

Codice Seconda figura

 

\begin{tikzpicture}
\begin{axis}[
axis x line=center,
axis y line=center,
xmin = -5,
xmax = 5.5,
ymin = -5,
ymax = 5.5,
xlabel = {$x$},
ylabel = {$y$},
extra x ticks = {0},
extra x tick label = {$\hspace{-0.9cm}0$},
y label style={anchor=north east}
]

\addplot[very thick,domain=-4:-1,samples=100,name path=ramoupleft] {sqrt(x^2-1)};
\addplot[red,very thick,domain=-4:-1,samples=100,name path=ramodownleft] {-sqrt(x^2-1)};
\addplot[very thick,domain=1:4,samples=100,name path=ramoupright] {sqrt(x^2-1)};
\addplot[red,very thick,domain=1:4,samples=100,name path=ramodownright] {-sqrt(x^2-1)};

\addplot[thin, samples=10,name path=asse,domain=-4:4] {0};
\addplot[thin, samples=10,white,name path=assesup,domain=-4:4] {4};
\addplot[thin, samples=10,white,name path=asseinf,domain=-4:4] {-4};
\addplot[black] (0,-4) -- (0,4);

\addplot[tau] fill between [of=ramoupleft and assesup, soft clip={domain=-4:-1}];
\addplot[tau] fill between [of=ramoupright and assesup, soft clip={domain=1:4}];
\addplot[tau] fill between [of=asseinf and ramodownleft, soft clip={domain=-4:-1}];
\addplot[tau] fill between [of=asseinf and ramodownright, soft clip={domain=1:4}];

\addplot[tau] fill between [of=asse and assesup, soft clip={domain=-1:1}];
\addplot[tau] fill between [of=asse and asseinf, soft clip={domain=-1:1}];

\addplot[black] coordinates {(1.7,3)} node[below,rotate=45] {$y=\sqrt{x^2-1}$};
\addplot[black] coordinates {(-3.1,-2.9)} node[red,below,rotate=42] {$y=-\sqrt{x^2-1}$};
\end{axis}
\end{tikzpicture}

Codice terza figura

 

\begin{tikzpicture}
\begin{axis}[
axis x line=center,
axis y line=center,
xmin = -5,
xmax = 5.5,
ymin = -5,
ymax = 5.5,
xlabel = {$x$},
ylabel = {$y$},
extra x ticks = {0},
extra x tick label = {$\hspace{-0.9cm}0$},
y label style={anchor=north east}
]

\addplot[very thick,domain=-4:-1,samples=100,name path=ramoupleft] {sqrt(x^2-1)};
\addplot[very thick,domain=-4:-1,samples=100,name path=ramodownleft] {-sqrt(x^2-1)};
\addplot[very thick,domain=1:4,samples=100,name path=ramoupright] {sqrt(x^2-1)};
\addplot[very thick,domain=1:4,samples=100,name path=ramodownright] {-sqrt(x^2-1)};

\addplot[thin, samples=10,name path=asse,domain=-4:4] {0};
\addplot[thin, samples=10,white,name path=assesup,domain=-4:4] {4};
\addplot[thin, samples=10,white,name path=asseinf,domain=-4:4] {-4};
\addplot[black] (0,-4) -- (0,4);

\addplot[very thick,domain=-4:4,samples=100,name path=ramosuperiore] {sqrt(x^2+1)};
\addplot[very thick,domain=-4:4,samples=100,name path=ramoinferiore] {-sqrt(x^2+1)};
\addplot[very thick,domain=-4:-1,samples=100,name path=ramoupleft] {sqrt(x^2-1)};
\addplot[very thick,domain=-4:-1,samples=100,name path=ramodownleft] {-sqrt(x^2-1)};
\addplot[very thick,domain=1:4,samples=100,name path=ramoupright] {sqrt(x^2-1)};
\addplot[very thick,domain=1:4,samples=100,name path=ramodownright] {-sqrt(x^2-1)};

\addplot[tau] fill between [of=ramosuperiore and ramoupleft, soft clip={domain=-4:-1}];
\addplot[tau] fill between [of=ramodownleft and ramoinferiore, soft clip={domain=-4:-1}];
\addplot[tau] fill between [of=ramosuperiore and ramoupright, soft clip={domain=1:4}];
\addplot[tau] fill between [of=ramoinferiore and ramodownright, soft clip={domain=1:4}];
\addplot[tau] fill between [of=ramoinferiore and asse, soft clip={domain=-1:1}];
\addplot[tau] fill between [of=ramosuperiore and asse, soft clip={domain=-1:1}];
\end{axis}
\end{tikzpicture}

 

Codice quarta figura

 

\begin{tikzpicture}
\begin{axis}[
axis x line=center,
axis y line=center,
xmin = -5,
xmax = 5.5,
ymin = -5,
ymax = 5.5,
xlabel = {$x$},
ylabel = {$y$},
extra x ticks = {0},
extra x tick label = {$\hspace{-0.9cm}0$},
y label style={anchor=north east}
]

\addplot[very thick,domain=-5:5,samples=100,name path=parabola] {x^2-4*x};
\addplot[thin, samples=10,name path=asse,domain=-5:5] {0};
\addplot[thin,white, samples=10,name path=assesup,domain=-5:5] {5.5};
\addplot[thin,white, samples=10,name path=asseinf,domain=-5:5] {-5};
\addplot[black] (0,5.5) -- (0,-5);

\addplot[black] coordinates {(3.7,3.7)} node[below,rotate=75] {$y=x^2-4x$};

\addplot[rosaantico] fill between [of=parabola and asse, soft clip={domain=4:5}];
\addplot[rosaantico] fill between [of=parabola and asse, soft clip={domain=-5:0}];
\addplot[rosaantico] fill between [of=parabola and asseinf, soft clip={domain=-5:5}];
\addplot[azzurro] fill between [of=assesup and parabola, soft clip={domain=-2:5}];
\end{axis}
\end{tikzpicture}

 

Codice quinta figura

 

\begin{tikzpicture}
\begin{axis}[
axis x line=center,
axis y line=center,
xmin = -5,
xmax = 5.5,
ymin = -5,
ymax = 5.5,
xlabel = {$x$},
ylabel = {$y$},
extra x ticks = {0},
extra x tick label = {$\hspace{-0.9cm}0$},
y label style={anchor=north east}
]

\addplot[very thick,domain=-5:5,samples=100,name path=rettapos] {2*x-1};
\addplot[very thick,domain=-5:5,samples=100,name path=rettaneg] {-2*x+1};
\addplot[thin, samples=10,name path=asse,domain=-5:5] {0};
\addplot[thin,white, samples=10,name path=assesup,domain=-5:5] {5.5};
\addplot[thin,white, samples=10,name path=asseinf,domain=-5:5] {-5};
\addplot[black] (0,5.5) -- (0,-5);

\addplot[black] coordinates {(2.5,3.7)} node[below,rotate=60] {$y=2x-1$};
\addplot[black] coordinates {(-1.5,3.7)} node[below,rotate=-60] {$y=-2x+1$};

\addplot[rosaantico] fill between [of=rettapos and asse, soft clip={domain=0.5:5.5}];
\addplot[rosaantico] fill between [of=rettaneg and asse, soft clip={domain=0.5:5.5}];
\addplot[azzurro] fill between [of=assesup and rettapos, soft clip={domain=0:3.5}];
\addplot[azzurro] fill between [of=assesup and asse, soft clip={domain=0:-5.5}];
\addplot[azzurro] fill between [of=asseinf and asse, soft clip={domain=0:-5.5}];
\addplot[azzurro] fill between [of=asseinf and rettaneg, soft clip={domain=0:3.5}];
\end{axis}
\end{tikzpicture}

 

Codice sesta figura

 

\begin{tikzpicture}
\begin{axis}[
axis x line=center,
axis y line=center,
xmin = -11.5,
xmax = 11.5,
ymin = -11.5,
ymax = 11.5,
xlabel = {$x$},
ylabel = {$y$},
extra x ticks = {0},
extra x tick label = {$\hspace{-0.9cm}0$},
y label style={anchor=north east}
]

\addplot[very thick,domain=-11.5:11.5,samples=100,name path=parabola] {x^2-4*x};
\addplot[very thick,domain=-11.5:11.5,samples=100,name path=rettapos] {2*x-1};
\addplot[very thick,domain=-11.5:11.5,samples=100,name path=rettaneg] {-2*x+1};
\addplot[thin, samples=10,name path=asse,domain=-11.5:11.5] {0};
\addplot[thin,white, samples=10,name path=assesup,domain=-11.5:11.5] {11.5};
\addplot[thin,white, samples=10,name path=asseinf,domain=-11.5:11.5] {-11.5};
\addplot[black] (0,11.5) -- (0,-11.5);
\addplot +[mark=none, name path=as] coordinates {(-3, -11.5) (-3, 11.5)};

\addplot[azzurro] fill between [of=parabola and asse, soft clip={domain=4:11.5}];
\addplot[azzurro] fill between [of=assesup and rettapos, soft clip={domain=0:11.5}];
\addplot[azzurro] fill between [of=parabola and rettaneg, soft clip={domain=2.5:4}];
\addplot[azzurro] fill between [of=rettaneg and asse, soft clip={domain=4:11.5}];
\addplot[azzurro] fill between [of=rettapos and parabola, soft clip={domain=0.2:0.5}];
\addplot[azzurro] fill between [of=rettaneg and parabola, soft clip={domain=0.5:2.5}];
\addplot[azzurro] fill between [of=asseinf and asse, soft clip={domain=-3:-11.5}];
\addplot[azzurro] fill between [of=rettaneg and asse, soft clip={domain=-3:-11.5}];
\addplot[azzurro] fill between [of=rettaneg and assesup, soft clip={domain=-3:-11.5}];
\addplot[azzurro] fill between [of=rettaneg and parabola, soft clip={domain=0:-0.2}];
\addplot[rosaantico] fill between [of=rettaneg and asse, soft clip={domain=-0.2:-3}];
\addplot[rosaantico] fill between [of=parabola and asse, soft clip={domain=-0.2:0}];
\addplot[rosaantico] fill between [of=rettaneg and assesup, soft clip={domain=-0.2:-3}];
\addplot[azzurro] fill between [of=assesup and parabola, soft clip={domain=0:-1.9}];
\addplot[rosaantico] fill between [of=asseinf and parabola, soft clip={domain=0.2:2.5}];
\addplot[rosaantico] fill between [of=asseinf and rettaneg, soft clip={domain=2.5:6}];
\addplot[rosaantico] fill between [of=asseinf and rettapos, soft clip={domain=0:0.2}];
\addplot[rosaantico] fill between [of=rettapos and parabola, soft clip={domain=4:5.6}];
\addplot[rosaantico] fill between [of=rettapos and asse, soft clip={domain=0.5:4}];
\addplot[rosaantico] fill between [of=rettapos and parabola, soft clip={domain=0:0.2}];
\addplot[rosaantico] fill between [of=rettaneg and asse, soft clip={domain=0.5:2.5}];
\addplot[rosaantico] fill between [of=parabola and asse, soft clip={domain=2.5:4}];
\addplot[rosaantico] fill between [of=asseinf and rettapos, soft clip={domain=0:-3}];
\addplot[rosaantico] fill between [of=rettapos and asse, soft clip={domain=0:-3}];
%\addplot[azzurro] fill between [of=asseinf and asse, soft clip={domain=0:-5.5}];
%\addplot[azzurro] fill between [of=asseinf and rettaneg, soft clip={domain=0:3.5}];
\end{axis}
\end{tikzpicture}