How to draw a complicated smooth curve

Question

I want to make each of the bending very smooth. Only criterion to draw the curve is that it starts from (1,2.5) and ends at (1,2.75). No equation of the curve given. I failed to do that. Please help.
documentclass[tikz,border=13mm]{standalone}
usetikzlibrary{arrows.meta,decorations.markings}
usetikzlibrary{calc}
%pgfplotsset{ticks=none}
usepackage{pgfplots}
pgfplotsset{compat=1.16}
begin{document}
     begin{axis}[name=MyAxis,grid=major,grid style=dotted , xmin=0, xmax=12, ymin=0, ymax=5,
          xlabel=$xrightarrow$, ylabel={$y rightarrow$}, 
                  %xtick = {0,.3479,1},  xticklabels = {,$x_1$,},
                    %ytick = {0,0.015,0.0414,.4}, yticklabels={,,,},  %yticklabels=empty,
         scale=1, restrict y to domain=0:5,clip=false]
    draw  (1,0) -- (1,3);
    addplot[color=red,smooth,thick,-] coordinates  {
    (1,2.5) (.3,2) (1,.8) (5,0.5) (7,.75) (7.75,1.15) (8.25,1.75)  (8,2.5) (7,3) (5,3.2) (3.75,3.15) (2.5,3) (1,2.75)};
            end{axis}
end{tikzpicture}
end{document}

DJP · Answer

You could draw[color=red] plot [smooth cycle]  for a better result:
documentclass[tikz,border=13mm]{standalone}
usetikzlibrary{arrows.meta,decorations.markings}
usetikzlibrary{calc}
%pgfplotsset{ticks=none}
usepackage{pgfplots}
pgfplotsset{compat=1.16}
begin{document}
    begin{tikzpicture}[>=stealth,declare function={f(x)=(10.5-x)/(10.5);}]
 begin{axis}[name=MyAxis,grid=major,grid style=dotted , xmin=0, xmax=12, ymin=0, ymax=5,
          xlabel=$xrightarrow$, ylabel={$y rightarrow$}, 
                  %xtick = {0,.3479,1},  xticklabels = {,$x_1$,},
                    %ytick = {0,0.015,0.0414,.4}, yticklabels={,,,},      %yticklabels=empty,
         scale=1, restrict y to domain=0:5,clip=false]
    draw  (1,0) -- (1,3);
    draw[color=red] plot [smooth cycle] coordinates {
(1,2.5) (.3,2) (1,.8) (5,0.5) (7,.75) (7.75,1.15) (8.25,1.75)  (8,2.5) (7,3) (5,3.2) (3.75,3.15) (2.5,3) (1,2.75)};
            end{axis}
end{tikzpicture}
end{document}

The result running in Gummi is:

Without the line, the curve is:

Original code posted by user1942348 without the line:

How to draw a complicated smooth curve

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