\begin{tikzpicture}[line cap=round,line join=round,x=1cm,y=1cm]
\tikzset{
        every pin/.style={fill=yellow!50!white,rectangle,rounded corners=3pt,font=\tiny},
        small dot/.style={fill=black,circle,scale=0.3},}
\begin{axis}[
x=1.5cm,y=1.5cm,
axis lines=middle,
axis line style = {-latex},
xmin=-0.25,
xmax=4.2,
ymin=-0.25,
ymax=3,
ytick=\empty,
xtick=\empty,
xlabel=$x$,
ylabel=$y$,
extra y ticks={1.5},
 extra y tick style={
        tick label style={anchor=east}},
    extra y tick labels={$\displaystyle g$},
enlargelimits = true,
]
\draw [thick, draw=blue!50!black] 
        (axis cs: -0.05,1.5) -- (axis cs: 5.2,1.5);
\node[] at (axis cs:2.5,2.5) {$y=f(x)$};

\addplot[domain=1.1:4.4, green!50!black	, line width=1,samples=200] {1.5+(5*e^(-x))*(cos(deg(2*pi*x)))};

\end{axis}



\end{tikzpicture}