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\documentclass[tikz, border=10pt, ngerman,]{standalone}

\usepackage{babel} % Deutsche Übersetzung, Trennregeln
\usepackage[utf8]{inputenc} % erweiterter Eingabezeichensatz
\usepackage[T1]{fontenc} % erweiterter T1 Zeichenvorrat

%\usepackage[charter]{mathdesign}
\usepackage[scaled=1.5, charter]{newtxmath}

\begin{document}
	\begin{tikzpicture}[semithick, >=latex]
		\draw[->] (-3,.4) -- (11,.4) node [right=1ex] {$t$};
		\draw[->] (0,0) -- (0,3) node [above left] {$u(t)$};
		\draw[samples= 100, blue, very thick]
		[domain=-2.8:-2] plot (\x, {2*exp(-3*(\x+4))})
		[domain=-2:0] plot (\x, {2*(1-exp(-3*(\x+2)))})
		[domain=0:2] plot (\x, {2*exp(-3*\x)})
		[domain=2:4] plot (\x, {2*(1-exp(-3*(\x-2)))})
		[domain=4:6] plot (\x, {2*exp(-3*(\x-4))})
		[domain=6:8] plot (\x, {2*(1-exp(-3*(\x-6)))})
		[domain=8:10] plot (\x, {2*exp(-3*(\x-8))});
	\end{tikzpicture}
\end{document}

\documentclass[tikz, border=10pt, ngerman,]{standalone} 

\usepackage{babel} % Deutsche Übersetzung, Trennregeln 
\usepackage[utf8]{inputenc} % erweiterter Eingabezeichensatz 
\usepackage[T1]{fontenc} % erweiterter T1 Zeichenvorrat 

%\usepackage[charter]{mathdesign} 
\usepackage[scaled=1.5, charter]{newtxmath} 

\begin{document} 
\begin{tikzpicture}[semithick, >=latex]
  \draw[->] (-3,.4) -- (11,.4) node [right=1ex] {$t$}; 
  \draw[->] (0,0) -- (0,3) node [above left] {$u(t)$}; 
  %
  \newcommand\DX{0.05}
  \draw[samples= 100, blue, very thick,rounded corners=1pt] 
    plot [domain=-2.8:{-2-\DX}] (\x, {2*exp(-3*(\x+4))})
    --(-2,{2*exp(-6)})-- 
    plot [domain={-2+\DX}:{0-\DX}] (\x, {2*(1-exp(-3*(\x+2)))})
    --(0,{2*(1-exp(-6))})--
    plot [domain={0+\DX}:{2-\DX}] (\x, {2*exp(-3*\x)})
    --(2,{2*exp(-6)})--
    plot[domain={2+\DX}:{4-\DX}] (\x, {2*(1-exp(-3*(\x-2)))})
    --(4,{2*(1-exp(-6))})--
    plot [domain={4+\DX}:{6-\DX}] (\x, {2*exp(-3*(\x-4))})
    --(6,{2*exp(-6)})--
    plot [domain={6+\DX}:{8-\DX}] (\x, {2*(1-exp(-3*(\x-6)))})
    --(8,{2*(1-exp(-6))})--
    plot [domain={8+\DX}:10]  (\x, {2*exp(-3*(\x-8))})
  ;
\end{tikzpicture} 
\end{document}