Mfcttrf

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):

documentclassarticle
usepackagepgfplots
usepackagetikz

begindocument

begintikzpicture
 beginaxis[%
 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] $;
 addplot[thick, red, dashed] (x,4);
 endaxis
endtikzpicture

enddocument

Current output:

Desired output:

Using intersections TiKz library, following solution may be obtained.

documentclassarticle
usepackagepgfplots
usepackagetikz
usetikzlibraryintersections

begindocument
begintikzpicture
 beginaxis[%
 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] $;
 addplot[thick, red, dashed,name path=line,domain=-13:1] (x,4);
 path [name intersections=of=curve and line, by=a,b];
 path [name path=x](axis cs:-13,0)--(axis cs:7,0);
 path [name path=y1](a)|-(axis cs:0,-13);
 path [name path=y2](b)|-(axis cs:0,-13);
 path [name intersections=of=y1 and x, by=x1];
 path [name intersections=of=y2 and x, by=x2];
 draw [thick,dashed,red](a)--(x1);
 draw [thick,dashed,red](b)--(x2);
 addplot[very thick, red,dashed,domain=-13:1,name path=x8] (-x-8);
 path [name intersections=of=x8 and line, by=x3];
 path [name path=y3](x3)|-(axis cs:0,-13);
 path [name intersections=of=y3 and x, by=x4];
 draw [thick,dashed,red](x3)--(x4);
 node at (axis cs:2.5,4)$y=4$;
 node[blue] at (axis cs:-7,6) $;
 endaxis

endtikzpicture

enddocument