\documentclass{standalone}
\usepackage[polish]{babel}
\usepackage[utf8]{inputenc} 
\usepackage[T1]{fontenc}
\usepackage{fourier}
\usepackage{tikz}
\usetikzlibrary{arrows.meta,intersections}

\begin{document}

\begin{tikzpicture}
\clip (-0.5,-0.5) rectangle (4.7,4.7);
\draw[thick] [->] (0,0) -- (4.5,0) node [below] {$x$};
\draw[thick] [->] (0,0) -- (0,4.5) node [left] {$y$};
\draw[name path=l1] (0,1) .. controls (10,1) and (-6,3) .. (4,3);
\draw[name path=l2] (1,0) .. controls (1,10) and (3,-6) .. (3,4);

\fill [name intersections={of=l1 and l2, name=i, total=\j}] 
  \foreach \i in {1,...,\j} {(i-\i) circle (2pt)};
\draw[dashed] (i-1) -- (i-9);
\end{tikzpicture}

\end{document}