Positioning tick marks along x-axis in pgfplots

Question

I have a plot of a cubic polynomial. I want to have tick marks along the x-axis to show that the root is between -1 and 0. With the default positioning of tick marks, the label -1 would interfere with the plot. I want to place the labels -2 and -1 above the x-axis and the 1 and 2 below the xaxis. In particular, I would like the spacing of -2 and -1 above the x-axis to be the same as the spacing of 1 and 2 below the x-axis.

\documentclass[10pt]{amsart}

\usepackage{tikz}
\usetikzlibrary{calc,intersections,}

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


\usepackage{mathtools,array}

\begin{document}

\begin{tikzpicture}
\begin{axis}[width=3.5in, clip=false,
    axis lines=middle,
    xmin=-2.5,xmax=2.5, domain=-2:2,
    ymin=-10,ymax=12,
    restrict y to domain=-10:12,
    xtick={-2,-1},
    ticklabel style={font=\tiny, anchor=south},
    xticklabels={\makebox[0pt][r]{$\tiny-$}2, \makebox[0pt][r]{$\tiny-$}1},
    extra x ticks={1,2},
    extra x tick labels={1,2},
    extra x tick style={font=\tiny},
    ytick={\empty},
    xlabel=$x$,ylabel=$y$,
    axis line style={latex-latex},
    axis line style={shorten >=-7.5pt, shorten <=-7.5pt},
    xlabel style={at={(ticklabel* cs:1)},anchor=north west},
    ylabel style={at={(ticklabel* cs:1)},anchor=south west}
]

\addplot[samples=201, domain=-2:2] {x^3 + x + 1)} node[right,pos=1,font=\footnotesize]{$y = x^{3} + x + 1$};

\end{axis}
\end{tikzpicture}

\end{document}

Answer 1

Applying tick label style={below} will position the label below at the correct default distance from the x-axis:

Notes:

• Font \tiny is not valid in math mode.
• Not sure what you were doing with the \makebox in the xticklabel style so have removed that.

• It appears that the default distance of the tick labels is different if the label is above, or below the axis. You can see this if you replace

  ticklabel style={font=\tiny, above}
  

  with

  ticklabel style={font=\tiny, below}
  

  I am not sure why these the two default settings are different. To tweak this, I added a yshift=0.5ex to the extra x tick style.

Code:

\documentclass[border=2pt]{standalone}

\usepackage{tikz}
\usetikzlibrary{calc,intersections,}

\usepackage{pgfplots}
\pgfplotsset{compat=newest}


\usepackage{mathtools,array}

\begin{document}

\begin{tikzpicture}
\begin{axis}[width=3.5in, clip=false,
    axis lines=middle,
    xmin=-2.5,xmax=2.5, domain=-2:2,
    ymin=-10,ymax=12,
    restrict y to domain=-10:12,
    xtick={-2,-1},
    ticklabel style={font=\tiny, above},
    xticklabels={$-2$, $-1$},% <--- corrected
    extra x ticks={1,2},
    extra x tick labels={1,2},
    extra x tick style={tick label style={red, below, yshift=0.5ex}},% <--- added "tick label style"
    ytick={\empty},
    xlabel=$x$,ylabel=$y$,
    axis line style={latex-latex},
    axis line style={shorten >=-7.5pt, shorten <=-7.5pt},
    xlabel style={at={(ticklabel* cs:1)},anchor=north west},
    ylabel style={at={(ticklabel* cs:1)},anchor=south west}
]

\addplot[samples=201, domain=-2:2] {x^3 + x + 1)} 
        node[right,pos=1,font=\footnotesize]{$y = x^{3} + x + 1$};

\end{axis}
\end{tikzpicture}

\end{document}