\documentclass{standalone}
\standaloneconfig{margin=2mm 2mm 2mm 2mm}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}

\begin{document}

\begin{tikzpicture}[scale=1.00]
    \begin{axis}[axis lines=center,
		xlabel={$x$},
		ylabel={$y$},
		xtick=\empty,ytick=\empty,
    xmin=-2.5,xmax=2.5,
    ymin=-0.1,ymax=1,
    axis line style={dashed},
		samples=200]
     \begin{scope}
            \clip (-2.2,-0.1) rectangle (2.2,1); % Define clipping path
            \draw[red, thick,looseness=0.4]
               (-2.5,1) to[out=0,in=180] (-2,0)
                        to[out=0,in=180] (-1,0.60)
                        to[out=0,in=180] (0,0)
                        to[out=0,in=180] (1,0.60)
                        to[out=0,in=180] (2,0)
                        to[out=0,in=180] (2.5,0.5); % Original curve path
      \end{scope}
      \node[below] at (2,0) {$e$};
      \node[below] at (-2,0) {$-e$};
      \node[below left] at (0,0) {\tiny O};
     \end{axis}
     \node[above] at (3.5,-0.5) {fonction périodique paire};
\end{tikzpicture}
\end{document}