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I have drawn the following figure in Mathematica. It is plot of y <= 1/x

enter image description here

But when I inserted it in latex using \begin{figure}, it was inserted there but I could not control its position in my document. Sometimes it moves into the unwanted position.

So, I thought if I could draw the figure in Latex using tikz. Actually, I want to draw the following figure ...

enter image description here

Can I draw the same graph as above in Latex?

Please help me.

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If you want to draw it in TikZ only, without using the axis environment (which I don't use, generally), here's a way to do that. It's what I use for my students.

fill under the inverse function

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{arrows.meta}

\begin{document}
    \begin{tikzpicture}
        \def\xmin{-9} \def\xmax{8}
        \def\ymin{-4} \def\ymax{6}
        \def\Mgrid{1} \def\mgrid{0.2}
        
        \def\f{1/x}
                
        \draw[cyan!20,thin] (\xmin,\ymin) grid[step=\mgrid] (\xmax,\ymax);
        \draw[cyan] (\xmin,\ymin) grid[step=\Mgrid] (\xmax,\ymax);
        \draw[-Stealth] (\xmin,0) -- (\xmax,0);
        \draw[-Stealth] (0,\ymin) -- (0,\ymax);
        \foreach \x in {\xmin,...,-1,1,2,...,\xmax} \node[below] at (\x,0) {\footnotesize \strut \x};
        \foreach \y in {\ymin,...,-1,1,2,...,\ymax} \node[left] at (0,\y) {\footnotesize \strut \y};
        
        \clip (\xmin,\ymin) rectangle (\xmax,\ymax);
        
        \fill[red,opacity=0.3] (\xmin,\ymin) -- plot[domain=\xmin:-0.01,samples=100] ({\x}, {1/\x}) -- cycle;       
        \draw[thick,domain=\xmin:-0.01,red,samples=100] plot ({\x}, {1/\x});
        
        \fill[red,opacity=0.3] (0,\ymin) -- (0,\ymax) -- plot[domain=0.01:\xmax,samples=100] ({\x}, {1/\x}) -- (\xmax,\ymin) -- cycle;      
        \draw[thick,domain=0.01:\xmax,red,samples=100] plot ({\x}, {1/\x});
        
    \end{tikzpicture}
\end{document}

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