Gdtyjr

I'm trying to do something similar to this epsilon-delta graph I've found. Specifically, I'd like to copy the placements and arrows, like the L+e and L-e coming out of L. Same thing with the x0 + d and x0-d coming out of the x0. Can someone help me with this? This is what I have so far.

begintikzpicture
beginaxis[
,
 legend pos=north east,
 axis x line=middle,
 axis y line=middle,
 x tick label style=/pgf/number format/fixed,
 /pgf/number format/fixed zerofill,
 /pgf/number format/precision=1,
 y tick label style=/pgf/number format/fixed,
 /pgf/number format/fixed zerofill,
 /pgf/number format/precision=1,
 grid = major,
 width=8cm, 
 height=6cm,
 grid style=dashed, gray!30,
 xmin=0 , % start the diagram at this x-coordinate
 xmax= 4, % end the diagram at this x-coordinate
 ymin= 0, % start the diagram at this y-coordinate
 ymax= 11, % end the diagram at this y-coordinate
%axis background/.style=fill=white,
 xlabel=$x$,
 ylabel=$f(x)$,
 tick align=outside,
 enlargelimits=false]
% plot the stirling-formulae
%addplot[domain=0:200, red, ultra thick,samples=100] K/(1 + ((K-X0)/X0) * exp(r*x)) ;
addplot[domain=0:200, red, ultra thick,samples=100] 3*x-1 ;

addplot[line width=1pt, dashed, mark=none, black] coordinates (0,8) (3,8);
addplot[line width=1pt, dashed, mark=none, black] coordinates (3,0) (3,8);
addplot[line width=1pt, dashed, mark=none, blue] coordinates (3.33,0) (3.333,9);
addplot[line width=1pt, dashed, mark=none, blue] coordinates (2.666,7) (2.666,0);
addplot[line width=1pt, dashed, mark=none, blue] coordinates (2.666,7) (0,7);
addplot[line width=1pt, solid, mark=none, blue] coordinates (3.333,9) (0,9);
addplot[holdot] coordinates(60,8.66);

% 1addlegendentry$f(x) = 10 sin (x)$

endaxis


endtikzpicture

which gives