\documentclass[12pt]{article}
\usepackage{tikz,pgfplots}
\usepackage{amsmath}
\begin{document}
\begin{center}
	\begin{tikzpicture}
		\begin{axis} [xlabel = $x$, ylabel = $f(x)$, axis lines = left,ticks=none]
		\end{axis}
		\fill [red] (2,1.5) circle (1.5mm);
		\fill [red] (3,2.8) circle (1.5mm);
		\fill [red] (4.5,4.6) circle (1.5mm);
		\draw [dashed,blue, ultra thin] (2,0)--(2,1.3);
		\draw [dashed,blue, ultra thin] (0,1.5)--(1.8,1.5);
		\draw [dashed,blue, ultra thin] (3,0)--(3,2.6);
		\draw [dashed,blue, ultra thin] (0,2.8)--(2.8,2.8);
		\draw [dashed,blue, ultra thin] (4.5,0)--(4.5,4.45);
		\draw [dashed,blue, ultra thin] (0,4.6)--(4.3,4.6) ;
	\end{tikzpicture}
\end{center}
\end{document}