LaTeX Forum

\documentclass[a4paper,draft]{scrartcl}
\usepackage[utf8]{inputenc} 
\usepackage{tikz}
\usepackage[left=2cm,right=2cm,top=2cm,bottom=2cm]{geometry}

\begin{document}
    
\begin{tikzpicture}
   
 \draw[step=.5cm, very thin, black!20] (-6,-3) grid (10,13);
 \draw[->, thick] (-5,0) -- (7,0) node[right] {$x$};
 \draw[->, thick] (0,0) -- (0,11) node[above] {$f(x)$};

    \foreach \x in {-4,...,-1}
    \draw[] (\x,0) -- (\x,-0.1) node[below] {\x};

    \foreach \x in {7,...,1}
    \draw[] (\x,0) -- (\x,-0.1) node[below] {\x};

    \foreach \y in {10,...,1}
    \draw[] (0,\y) -- (-0.1,\y) node[left] {\y};

\draw[smooth,domain=-3:3] plot(\x,{\x*\x}) node[right] {$f(x)=x^2$}; 
 
\draw[smooth,domain=0:6,samples=150] plot(\x,{sqrt(\x)}) node[right] {$f(x)=\sqrt x =x^\frac{1}{2}$}; 

%\draw[smooth,domain=0:2,samples=150] plot(\x,{pow(\x,0.5)}) node[right] {$f(x)=x^\frac{1}{2}$}; 

\draw[red,dashed] (1,0) -- (1,1) -- (0,1);
\draw[red,dashed] (2,0) -- (2,4) -- (0,4);
\draw[red,dashed] (3,0) -- (3,9) -- (0,9);

\end{tikzpicture}
\end{document}

pow(x,y)
\pgfmathpow{x}{y}
Raises x to the power of y. For greatest accuracy y should be an integer. If it is not an integer the actual calculation will be an approximation of $\exp ^{y \ln (x)}$.