Arbitrary Curve in Tikz

How can I improve this curve? Why do the arrows ruin the left side but keep the right side smooth? All suggestions welcome.

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=.6,cap=round]
\tikzset{axes/.style={}}
% The graphic
\begin{scope}[style=axes]
\draw[->] (-5,0) -- (5,0) node[below] {$x$};
\draw[->] (0,-3)-- (0,5) node[left] {$y$};
%\draw [gray!50]  (-5,3) -- (-2.5,1) -- (2.5,4) -- (5,-1);
\draw [red,thick,<->] plot [smooth,samples=200, tension=1] coordinates {
(-5,4) (-2.5,1) (2.5,4) (5,-1)};
\end{scope}
\end{tikzpicture}
\end{document}


• @Marmot yes I saw that but forgot to delete. If you remove <-> from the draw command there is a less "kink" in the output on the left. I was not sure why? Your hobby library allows the end arrows, so I will mark answered now – MathScholar Nov 15 '18 at 12:13
• I see. I expanded my answer by adding a explanation why that happens, hand how it can be prevented. – user121799 Nov 15 '18 at 14:55
• @Marmot, thank you for getting back to me on this. I will start using the second answer but look into the hobby package later. Again Thanks Marmot! – MathScholar Nov 16 '18 at 0:39

I do not precisely understand what you mean by "Why do the arrows ruin the left side but keep the right side smooth? ". However, this is just to say that there are many possible ways to draw smooth curves with TikZ. A rather powerful way is to employ the hobby library.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{hobby}
\begin{document}
\begin{tikzpicture}[scale=.6,cap=round,
tangent/.style={%
in angle={(180+#1)} ,
Hobby finish ,
designated Hobby path=next , out angle=#1,
}]
\tikzset{axes/.style={}}
% The graphic
\begin{scope}[style=axes]
\draw[->] (-5,0) -- (5,0) node[below] {$x$};
\draw[->] (0,-3)-- (0,5) node[left] {$y$};
%\draw [gray!50]  (-5,3) -- (-2.5,1) -- (2.5,4) -- (5,-1);
\draw [red,thick,<->,use Hobby shortcut]
([tangent=-80]-5,4)  .. (-2.5,1) ..  (2.5,4) .. ([tangent=-80]5,-1);
\end{scope}
\end{tikzpicture}
\end{document}


Does this come closer to what you want to achieve?

ADDENDUM: You are asking about the distortion you get when you add or remove an arrow. The effect you are referring to is clearly visible as the difference between the red and blue curves in

\documentclass{article}
\usepackage{tikz}
%\usetikzlibrary{bending}
\begin{document}
\begin{tikzpicture}[scale=.6,cap=round]
\tikzset{axes/.style={}}
% The graphic
\begin{scope}[style=axes]
\draw[->] (-5,0) -- (5,0) node[below] {$x$};
\draw[->] (0,-3)-- (0,5) node[left] {$y$};
%\draw [gray!50]  (-5,3) -- (-2.5,1) -- (2.5,4) -- (5,-1);
\draw [red,thick,<->] plot [smooth,tension=1] coordinates {
(-5,4) (-2.5,1) (2.5,4) (5,-1)};
\draw [blue,thick,-] plot [smooth,tension=1] coordinates {
(-5,4) (-2.5,1) (2.5,4) (5,-1)};
\end{scope}
\end{tikzpicture}
\end{document}


This effect is due to the fact that a (standard) arrow inserts a stretch of straight (as opposed to curved) path. You can simply get rid of it by activating \usetikzlibrary{bending}, i.e. by removing the % in front of it.

Of course, if you have longer arrows, you want to make sure that you load arrows.meta as well and pass bend to the options of the arrow, e.g. 

 \draw [red,thick,{Latex[bend,length=5pt]}-{Latex[bend,length=5pt]}] plot [smooth,tension=1] coordinates {
(-5,4) (-2.5,1) (2.5,4) (5,-1)};
`
• Thanks Marmot, this output is what I need. Again the program I posted works without end arrows, but this Hobby library is new to me as well! – MathScholar Nov 15 '18 at 12:23