We give a basic template for graphs in TikZ.
You do it like this:
\begin{image}
\begin{tikzpicture}
\begin{axis}[
xmin=-6.4,
xmax=6.4,
ymin=-1.2,
ymax=1.2,
axis lines=center,
xlabel=$x$,
ylabel=$y$,
every axis y label/.style={at=(current axis.above origin),anchor=south},
every axis x label/.style={at=(current axis.right of origin),anchor=west},
]
\addplot [ultra thick, penColor, smooth] {sin(deg(x))};
\end{axis}
\end{tikzpicture}
\end{image}
You can add more plots, like so:
\begin{image}
\begin{tikzpicture}
\begin{axis}[
xmin=-6.4,
xmax=6.4,
ymin=-1.2,
ymax=1.2,
axis lines=center,
xlabel=$x$,
ylabel=$y$,
every axis y label/.style={at=(current axis.above origin),anchor=south},
every axis x label/.style={at=(current axis.right of origin),anchor=west},
]
\addplot [ultra thick, penColor, smooth] {sin(deg(x))};
\addplot [ultra thick, penColor2, smooth,domain] {cos(deg(x))};
\addplot [ultra thick, penColor3, smooth] {1};
\addplot [ultra thick, penColor4, smooth] {-1};
\addplot [ultra thick, penColor5, smooth,domain=-1:1] {x};
\end{axis}
\end{tikzpicture}
\end{image}
You can make an array of plots like this:
\begin{image}
\begin{tikzpicture}
\begin{axis}[
xmin=-10.3,xmax=10.3,ymin=-10.3,ymax=10.3,
clip=true,
unit vector ratio*=1 1 1,
axis lines=center,
grid = major,
ytick={-21,-18,...,21},
xtick={-21,-18,...,21},
xlabel=$x$, ylabel=$y$,
y tick label style={anchor=west},
every axis y label/.style={at=(current axis.above origin),anchor=south},
every axis x label/.style={at=(current axis.right of origin),anchor=west},
]
\addplot[very thick,penColor,domain=-10.3:-3,samples=50] plot{x/sqrt(x^2-9)};
\addplot[very thick,penColor,domain=3:10.3,samples=500] plot{x/sqrt(x^2-9)};
\node at (axis cs:6,6) {\huge$A$};
\end{axis}
\end{tikzpicture}\quad
\begin{tikzpicture}
\begin{axis}[
xmin=-10.3,xmax=10.3,ymin=-10.3,ymax=10.3,
clip=true,
unit vector ratio*=1 1 1,
axis lines=center,
grid = major,
ytick={-21,-18,...,21},
xtick={-21,-18,...,21},
xlabel=$x$, ylabel=$y$,
y tick label style={anchor=west},
every axis y label/.style={at=(current axis.above origin),anchor=south},
every axis x label/.style={at=(current axis.right of origin),anchor=west},
]
\addplot[very thick,penColor,domain=-10.3:-0.08,samples=50] plot{1/x};
\addplot[very thick,penColor,domain=0.08:10.3,samples=50] plot{1/x};
\node at (axis cs:6,6) {\huge$B$};
\end{axis}
\end{tikzpicture}
\end{image}
\begin{image}
\begin{tikzpicture}
\begin{axis}[
xmin=-10.3,xmax=10.3,ymin=-10.3,ymax=10.3,
clip=true,
unit vector ratio*=1 1 1,
axis lines=center,
grid = major,
ytick={-21,-18,...,21},
xtick={-21,-18,...,21},
xlabel=$x$, ylabel=$y$,
y tick label style={anchor=west},
every axis y label/.style={at=(current axis.above origin),anchor=south},
every axis x label/.style={at=(current axis.right of origin),anchor=west},
]
\addplot[very thick,penColor,domain=-10.3:-0.08,samples=50] plot{1/x-1};
\addplot[very thick,penColor,domain=0.08:10.3,samples=50] plot{1/x+1};
\node at (axis cs:6,6) {\huge$C$};
\end{axis}
\end{tikzpicture}\quad
\begin{tikzpicture}
\begin{axis}[
xmin=-10.3,xmax=10.3,ymin=-10.3,ymax=10.3,
clip=true,
unit vector ratio*=1 1 1,
axis lines=center,
grid = major,
ytick={-21,-18,...,20},
xtick={-21,-18,...,20},
xlabel=$x$, ylabel=$y$,
y tick label style={anchor=west},
every axis y label/.style={at=(current axis.above origin),anchor=south},
every axis x label/.style={at=(current axis.right of origin),anchor=west},
]
\addplot[very thick,penColor,domain=-10.3:-3,samples=50] plot{-x/sqrt(x^2-9)-2};
\addplot[very thick,penColor,domain=3:10.3,samples=800] plot{-x/sqrt(x^2-9)+2};
\node at (axis cs:6,6) {\huge$D$};
\end{axis}
\end{tikzpicture}
\end{image}