We give a basic template for graphs in TikZ.

If you want to produce a simple graph, like this one:

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}