Displaying two graphs adjacent to each other with their x-axes aligned (Version 2)

Question

I have two graphs drawn using pgfplots. The graphs are drawn as I would like them to be drawn, and the x-axes are aligned, as I would like them to be aligned. There are three modifications that I need. First, the two graphs should be horizontally centered. Second, more (horizontal) space is needed between the two graphs. Third, a title needs to be centered over the y-axis of each graph. Something like the following code would be suitable.

\node[align=center, font=\bfseries, inner sep=0pt, above=3mm] at (current bounding box.north) {The graph of an \\ increasing function};

\node[align=center, font=\bfseries, inner sep=0pt, above=3mm] at (current bounding box.north) {The graph of a strictly \\ increasing function};

By the way, in the first graph, I have a horizontal line drawn along the x-axis between the origin and (1,0). Are the axes drawn with a width of 0.8pt? I used the option line width=1.2pt to draw this horizontal line. Is that typical when "drawing over" the axes?

\documentclass{amsart}

\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}


\begin{document}

\begin{tikzpicture}
\begin{axis}[width=3in,axis equal image, clip=false,
    xmin=-4,xmax=4,
    ymin=-4,ymax=4,
    restrict y to domain=-4:4,
    %enlargelimits={abs=1cm},
    xtick={\empty},ytick={\empty},
    axis lines=middle,
    axis line style={latex-latex},
    xlabel=$x$,ylabel=$y$,
    xlabel style={at={(ticklabel* cs:1)},anchor=north west},
    ylabel style={at={(ticklabel* cs:1)},anchor=south west}
]

\addplot [domain=-3:-2] {-3};
\addplot [domain=-2:-1] {-2};
\addplot [domain=-1:0] {-1};
\addplot [line width=1.2pt, domain=0:1] {0};
\addplot [domain=1:2] {1};
\addplot [domain=2:3] {2} node [pos=1, anchor=south west, font=\footnotesize] {$y=f(x)$};

\draw[fill] (-3,-3) circle [radius=1.5pt];
\draw[fill] (-2,-2) circle [radius=1.5pt];
\draw[fill] (-1,-1) circle [radius=1.5pt];
\draw[fill] (0,0) circle [radius=1.5pt];
\draw[fill] (1,1) circle [radius=1.5pt];
\draw[fill] (2,2) circle [radius=1.5pt];

\draw [fill=white] (-2,-3) circle [radius=1.5pt];
\draw [fill=white] (-1,-2) circle [radius=1.5pt];
\draw [fill=white] (0,-1) circle [radius=1.5pt];
\draw [fill=white] (1,0) circle [radius=1.5pt];
\draw [fill=white] (2,1) circle [radius=1.5pt];
\draw [fill=white] (3,2) circle [radius=1.5pt];

\end{axis}
\end{tikzpicture}
%
%
\begin{tikzpicture}
\begin{axis}[width=3in, clip=false,
    xmin=-3,xmax=3,
    ymin=-10,ymax=10,
    restrict y to domain=-8:8,
   % enlargelimits={abs=1cm},
    xtick={\empty},ytick={\empty},
    axis lines=middle,
    axis line style={latex-latex},
    xlabel=$x$,ylabel=$y$,
    xlabel style={at={(ticklabel* cs:1)},anchor=north west},
    ylabel style={at={(ticklabel* cs:1)},anchor=south west}
]
\addplot [domain=-2:2] {x^3} node [pos=1, anchor=west, font=\footnotesize] {$y=g(x)$};

\end{axis}
\end{tikzpicture}

\end{document}

Answer 1

All of these things are easily achievable by combining the plots into a single tikzpicture.

"First, the two graphs should be horizontally centered."

This is done by surrounding the tikzpicture environment with the center environment.

"Second, more (horizontal) space is needed between the two graphs."

By placing the two plots in the same tikzpicture, we can control their relative positioning by naming the first plot via the name = <name> option, and then setting the location of the second plot with at = (<name>.east). Adding anchor = west keeps the x-axis alignment. After doing this, the separation distance between the plots can be adjusted via xshift = <value>.

"Third, a title needs to be centered over the y-axis of each graph. "

We can just use the title = {<title>} option. Note that I added align = center in order to achieve the manual line break you wanted.

Update: Title positioning adjustments

We can add some options in the title style to place the title below the axis.

Code:

\documentclass{amsart}

\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}


\begin{document}

\begin{center}
\begin{tikzpicture}
\begin{axis}[width=3in,axis equal image, clip=false,
    xmin=-4,xmax=4,
    ymin=-4,ymax=4,
    restrict y to domain=-4:4,
    %enlargelimits={abs=1cm},
    xtick={\empty},ytick={\empty},
    axis lines=middle,
    axis line style={latex-latex},
    xlabel=$x$,ylabel=$y$,
    xlabel style={at={(ticklabel* cs:1)},anchor=north west},
    ylabel style={at={(ticklabel* cs:1)},anchor=south west},
    title style = {align = center, at = (current axis.south), anchor = north, yshift = -2em},
    title = {The graph of an \\ increasing function}, name = left
]

\addplot [domain=-3:-2] {-3};
\addplot [domain=-2:-1] {-2};
\addplot [domain=-1:0] {-1};
\addplot [line width=1.2pt, domain=0:1] {0};
\addplot [domain=1:2] {1};
\addplot [domain=2:3] {2} node [pos=1, anchor=south west, font=\footnotesize] {$y=f(x)$};

\draw[fill] (-3,-3) circle [radius=1.5pt];
\draw[fill] (-2,-2) circle [radius=1.5pt];
\draw[fill] (-1,-1) circle [radius=1.5pt];
\draw[fill] (0,0) circle [radius=1.5pt];
\draw[fill] (1,1) circle [radius=1.5pt];
\draw[fill] (2,2) circle [radius=1.5pt];

\draw [fill=white] (-2,-3) circle [radius=1.5pt];
\draw [fill=white] (-1,-2) circle [radius=1.5pt];
\draw [fill=white] (0,-1) circle [radius=1.5pt];
\draw [fill=white] (1,0) circle [radius=1.5pt];
\draw [fill=white] (2,1) circle [radius=1.5pt];
\draw [fill=white] (3,2) circle [radius=1.5pt];

\end{axis}
\begin{axis}[width=3in, clip=false,
    xmin=-3,xmax=3,
    ymin=-10,ymax=10,
    restrict y to domain=-8:8,
   % enlargelimits={abs=1cm},
    xtick={\empty},ytick={\empty},
    axis lines=middle,
    axis line style={latex-latex},
    xlabel=$x$,ylabel=$y$,
    xlabel style={at={(ticklabel* cs:1)},anchor=north west},
    ylabel style={at={(ticklabel* cs:1)},anchor=south west},
    title style = {align = center, inner sep = 0pt, above = 3mm},
    title = {The graph of a strictly \\ increasing function},
    at = (left.east), anchor = west, xshift = 2cm
]
\addplot [domain=-2:2] {x^3} node [pos=1, anchor=west, font=\footnotesize] {$y=g(x)$};

\end{axis}
\end{tikzpicture}
\end{center}

\end{document}

Output:

Answer 2

1. For bigger distance between graph just ad some space between the, for example \qquad or as it is in code below \hspace{4em} (or other distance according to your wish). Note: your graphs are not centered in text width (if this matter).

2. For title above graphs you need only to add to axis option title style={align=center, font=\bfseries} and title={... \\ ....}

3. Third wish is already achieved with measure in second item :-)

All this gives:

The complete code is:

\documentclass{amsart}
    \usepackage{pgfplots}
    \pgfplotsset{compat=1.11}


    \begin{document}
\begin{tikzpicture}
\begin{axis}[width=3in,axis equal image, clip=false,
    xmin=-4,xmax=4,
    ymin=-4,ymax=4,
    restrict y to domain=-4:4,
    %enlargelimits={abs=1cm},
    xtick={\empty},ytick={\empty},
    axis lines=middle,
    axis line style={latex-latex},
    xlabel=$x$,ylabel=$y$,
    xlabel style={at={(ticklabel* cs:1)},anchor=north east},
    ylabel style={at={(ticklabel* cs:1)},anchor=north east},
    title style={align=center, font=\bfseries},
    title={The graph of an \\ increasing function}
]

\addplot [domain=-3:-2] {-3};
\addplot [domain=-2:-1] {-2};
\addplot [domain=-1:0] {-1};
\addplot [line width=1.2pt, domain=0:1] {0};
\addplot [domain=1:2] {1};
\addplot [domain=2:3] {2} node [pos=1, anchor=south west, font=\footnotesize] {$y=f(x)$};

\draw[fill] (-3,-3) circle [radius=1.5pt];
\draw[fill] (-2,-2) circle [radius=1.5pt];
\draw[fill] (-1,-1) circle [radius=1.5pt];
\draw[fill] (0,0) circle [radius=1.5pt];
\draw[fill] (1,1) circle [radius=1.5pt];
\draw[fill] (2,2) circle [radius=1.5pt];

\draw [fill=white] (-2,-3) circle [radius=1.5pt];
\draw [fill=white] (-1,-2) circle [radius=1.5pt];
\draw [fill=white] (0,-1) circle [radius=1.5pt];
\draw [fill=white] (1,0) circle [radius=1.5pt];
\draw [fill=white] (2,1) circle [radius=1.5pt];
\draw [fill=white] (3,2) circle [radius=1.5pt];

\end{axis}
\end{tikzpicture}
%
\hspace{4em}
%
\begin{tikzpicture}
\begin{axis}[width=3in, clip=false,
    xmin=-3,xmax=3,
    ymin=-10,ymax=10,
    restrict y to domain=-8:8,
   % enlargelimits={abs=1cm},
    xtick={\empty},ytick={\empty},
    axis lines=middle,
    axis line style={latex-latex},
    xlabel=$x$,ylabel=$y$,
    xlabel style={at={(ticklabel* cs:1)},anchor=north east},
    ylabel style={at={(ticklabel* cs:1)},anchor=north east},
    title style={align=center, font=\bfseries},
    title={The graph of a strictly \\ increasing function}
]
\addplot [domain=-2:2] {x^3} node [pos=1, anchor=west, font=\footnotesize] {$y=g(x)$};

\end{axis}
\end{tikzpicture}
    \end{document}

About line widths: this depend on personal test. Different people, different taste ... If you liked more "bold" just increase their thickness. As I change position of axis labels according to my taste :-)

Edit: Little of topic: the first graph, as it is, can be drawn much simpler:

\documentclass{amsart}
    \usepackage{pgfplots}
    \pgfplotsset{compat=1.11}
    \usetikzlibrary{arrows.meta}

    \begin{document}
\begin{tikzpicture}[
    L/.style = {% as Line
                {Circle[width=1mm,length=1mm]}-%
                {Circle[width=1mm,length=1mm,open,line width=0.4pt]},
                shorten >=-0.6mm, shorten <=-0.6mm,
               }    ]
\begin{axis}[width=3in,axis equal image, clip=false,
    xmin=-4,xmax=4,
    ymin=-4,ymax=4,
    restrict y to domain=-4:4,
    %enlargelimits={abs=1cm},
    xtick={\empty},ytick={\empty},
    axis lines=middle,
    axis line style={latex-latex},
    xlabel=$x$,ylabel=$y$,
    xlabel style={at={(ticklabel* cs:1)},anchor=north east},
    ylabel style={at={(ticklabel* cs:1)},anchor=north east},
    title style={draw,align=center, font=\bfseries},
    title={The graph of an \\ increasing function}
]

\draw[red,L] (-3,-3) edge (-2,-3)
             (-2,-2) edge (-1,-2)
             (-1,-1) edge (0,-1)
             (0,0) edge[thick] (1,0)
             (1,1) edge (2,1)
             (2,2)  --  (3,2) node[anchor=south west,font=\footnotesize] {$y=f(x)$};

\end{axis}
\end{tikzpicture}
     \end{document}

As you see, omitted as all \addplot ... and separated draw of circles are replaced with lines with filled and open circles on the ends.

And on-topic: On positioning of nodes you have more possibilities:

• define anchor of node and say for example \node[anchor=south] at (<coordinate>) ... and node's anchor south will lie on <coordinate>

• use option above, for example \node[above] at (<coordinate>) ... and node will lie on the same place as before

• define anchor of node and after that use option above, for example \node[anchor=north,above] at (<coordinate>) ... and node will lie as before regardless that regarding to anchor one expect different (in this case above override anchor)

• define anchor of node after use of option above, for example: \node[above,anchor=north] at (<coordinate>) .... Now the node position will differ from before cases. On <coordinate> will lie node's anchor north

With drawing nodes border (as shown on figure) can help to see, where is text baseline. Its position in node is depend on text depth, if it is not extra defined. For details is very recommencement to read TikZ manual "17.4.4 Text Parameters: Height and Depth of Text" on page 226. and than "17.5 Positioning Nodes" on page 227.