Plot this function using tkz-fct

If you are happy with pgfplots instead of tkz-fct, then this would be a starting point:

documentclass[border=5mm]{standalone}

usepackage{pgfplots}

begin{document}
    begin{tikzpicture}
    begin{axis}[
    samples=100,
    ticks=none,
    xmin = 0, xmax = 2,
    ymin = 0, ymax = 4,
    domain=0:1.6,
    axis x line=bottom,
    axis y line=left,
    xlabel={$x$},
    ylabel={$y$},
    every axis x label/.style={
        at={(axis cs:2,0)},
        anchor=north,
    },
    every axis y label/.style={
        at={(axis cs:0,4)},
        anchor=east
    },
    legend style={
        at={(axis cs:-5.2,4)},
        anchor=west, font=scriptsize
    },
    declare function={f(x)=(x)^2;},
    ] 
    addplot[mark=none] {f(x)};
    
    draw (axis cs:0,{f(1.5)})coordinate(B) -- (axis cs:1.5,{f(1.5)}) -- (axis cs:1.5,0)coordinate(C);
    draw (axis cs:1.2,{f(1.2)}) -- (axis cs:1.2,0)coordinate(A)node[near end,left]{$S_1$};
    
    node[above] at (axis cs:1.6,{f(1.6)}) {$y=x^{p-1}$};
    
    node at (axis cs:0.7,1.6) {$S_2$};
    
    end{axis}
    node[anchor=north] at (A) {$A$};
    node[anchor=east] at (B) {$B$};
    node[anchor=north] at (C) {$C$};
    end{tikzpicture}
end{document}