\documentclass[varwidth=false, border=2pt]{standalone}

\usepackage{pgfplots}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}
    \begin{axis}[
        axis x line=middle,
        axis y line=middle,
        grid = major,
        width=16cm,
        height=8cm,
        grid style={dashed, gray!30},
        xmin=-1,     % start the diagram at this x-coordinate
        xmax= 1,    % end   the diagram at this x-coordinate
        ymin= 0,     % start the diagram at this y-coordinate
        ymax= 1.2,   % end   the diagram at this y-coordinate
        xlabel=x,
        ylabel=y,
		/pgfplots/xtick={-1, -0.5, ..., 1}, % make steps of length 0.5
		/pgfplots/ytick={0, 0.5, ..., 1}, % make steps of length 0.5
        tick align=outside,
        enlargelimits=false]
      % plot the function
	  \addplot[domain=-1:1, blue, ultra thick,samples=500] {x < -0.5 ? 0 : (x < 0.5 ? x +0.5 : 1)};
    \end{axis}
\end{tikzpicture}
\end{document}
