Mdthbs

Problem:

I have several minor issues that I can not seem to be able to solve.

1. Add and position labels to x/y-axis


2. Add dashed intersections


3. Show x/y-axis numbers for -1 and 1

Minimal Working Example (MWE):

documentclass{article}

usepackage{pgfplots}

usepackage{tikz}



begin{document}



begin{tikzpicture}

        begin{axis}[%

            axis on top = true,

            domain = -13:7,

            samples = 150,

            xmin=-13,

            xmax=7,

            ymin=-13,

            ymax=7,

            minor x tick num=4,

            minor y tick num=4,

            axis lines = middle,

            xtick distance = 5,

            xticklabel style = {font=footnotesize},

            yticklabel style = {font=footnotesize},

            xlabel = $x$,

            ylabel = $y$

            ]

            addplot[very thick, blue] {2*abs(x-1)-3*abs(x+2)} node[pos=-.7,left] {footnotesize $y=|2x-1|-3|x+2|$};

            addplot[thick, red, dashed] (x,4);

        end{axis}

end{tikzpicture}



end{document}

Current output:

Desired output:

Using intersections TiKz library, following solution may be obtained.

documentclass{article}

usepackage{pgfplots}

usepackage{tikz}

usetikzlibrary{intersections}



begin{document}

begin{tikzpicture}

        begin{axis}[%

            axis on top = true,

            domain = -13:7,

            samples = 150,

            xmin=-13,

            xmax=7,

            ymin=-13,

            ymax=7,

            minor x tick num=4,

            minor y tick num=4,

            axis lines = middle,

            xtick distance = 5,

            xticklabel style = {font=footnotesize},

            yticklabel style = {font=footnotesize},

            xlabel = $x$,

            ylabel = $y$,

        extra x ticks={-1, 1},

        extra y ticks={1},

            ]

            addplot[very thick, blue,name path=curve] {2*abs(x-1)-3*abs(x+2)};%

            % node[pos=-.7,left] {footnotesize $y=|2x-1|-3|x+2|$};

            addplot[thick, red, dashed,name path=line,domain=-13:1] (x,4);

            path [name intersections={of=curve and line, by={a,b}}];

            path [name path=x](axis cs:-13,0)--(axis cs:7,0);

           path [name path=y1](a)|-(axis cs:0,-13);

           path [name path=y2](b)|-(axis cs:0,-13);

           path [name intersections={of=y1 and x, by={x1}}];

           path [name intersections={of=y2 and x, by={x2}}];

           draw [thick,dashed,red](a)--(x1);

           draw [thick,dashed,red](b)--(x2);

 addplot[very thick, red,dashed,domain=-13:1,name path=x8] {(-x-8)};

 path [name intersections={of=x8 and line, by={x3}}];

 path [name path=y3](x3)|-(axis cs:0,-13);

 path [name intersections={of=y3 and x, by={x4}}];

 draw [thick,dashed,red](x3)--(x4);

 node at (axis cs:2.5,4){$y=4$};

 node[blue] at (axis cs:-7,6) {footnotesize $y=|2x-1|-3|x+2|$};

        end{axis}



end{tikzpicture}



end{document}