shadow in picture

Question

Can you help me with this function?

Answer 1

It is not clear, what is your problem: fill area where y>f(x) or definition of the function f(x) (the later is actually math problem).

In any case it is simpler to use pgfplots package (which is based on tikz package) than pure tikz package, where you need to draw axis, labels, etc. yourself.

Let me focused on shading. Using pgfplots package it can be done by use of fill between function defined in the pgfplotslibrary library:

\documentclass[border=3.141592]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\usepgfplotslibrary{fillbetween}
\begin{document}
    \begin{tikzpicture}
\begin{axis}[
declare function = {f(\x) = 3*(\x-1)+3;}, % here you define own function, 
                                          % for example  f(\x) = (\x-1)^3+1;, etc
    axis lines=center,
    xtick=\empty,   ytick=\empty,
    axis on top,
%
    label style={anchor=north east},
    xlabel=$x$,
    ylabel=$y$,
%
    domain=-3:3,  samples=101, no marks,
    xmin=-2, xmax=3,
    ymin=-3, ymax=3,
%
    every axis plot post/.append style={line width=1pt},
                ]
  \addplot +[name path=F]    {f(x)};
  \path     [name path=Y]
        (\pgfkeysvalueof{/pgfplots/xmin},0\pgfkeysvalueof{/pgfplots/ymin}) --
        (\pgfkeysvalueof{/pgfplots/xmin},\pgfkeysvalueof{/pgfplots/ymax}) 
            node[text=blue, below right=3mm] {$y\geq f(x)$};
  \addplot [fill=blue!10] fill between [of = F and Y]; % end of fillbetween
\end{axis}
    \end{tikzpicture}
\end{document}

In the case, that in above MWE you consider for function @Sebastiano suggestion, i.e. f(\x) = (\x-1)^3 +1 and change definition and observation domain to:

    domain=-2:3,  samples=101, no marks,
    xmin=-2, xmax=4,
    ymin=-2, ymax=3,

the obtained image is:

Answer 2

For fun, I propose this easy short code with pstricks:

\documentclass[11pt,svgnames, border=3pt]{standalone}
\usepackage{pst-plot}
\usepackage{sansmath}
\begin{document}
\begin{pspicture}(-3 ,-3)(3.5,3.2)
\sansmath
\psset{algebraic, plotpoints=500, labelsep=2pt}
\pscustom[fillstyle=solid, fillcolor=Lavender, linestyle=none]%
{\psline(-3,-3)(-1.442,-3)\psplot{-1.442}{1.442}{x^3} \psline(1.442,3)(-3,3)(-3,-3)}
\psplot[linewidth=1.2pt, linecolor=RoyalBlue,]{-1.442}{1.442}{x^3} 
\psaxes[ticks=none, labels=none, showorigin=false, arrows=->,arrowinset=0.12, linecolor=black] %
(-1,-1)(-3,-3)(3.2,3)[$x$, 0][$y$,180]
\rput(0,2.5){$\color{RoyalBlue}y\ge f(x)$}
\end{pspicture}
\end{document} 

Answer 3

My idea it is simple if you have a lot of difficulty to plot in TikZ: plot the function (x-1)^{3}+1 using Geogebra and you can define a shadow zone with a inequality. With Geogebra you can put all the labels in sans-serif font and export in TikZ, eventually making some corrections. At the end changed the tips with the classic arrow of tikz-cd.