Problem with axis when drawing a function plot using PGFplots

Question

Dear TeX StackExchange,

I am trying to plot two functions in the same grid. The code I currently have is below:

\begin{center}
\begin{tikzpicture}[scale=1, transform shape]
\begin{axis}[grid=both,
      mark = none,
      xmin = 0, ymin = 0,
      xmax = 16,ymax = 16,
      axis lines*=middle,
      enlargelimits,
      xtick={0,2,...,16},
      ytick={0,2,...,16}]
\addplot[red, domain=0:5, samples=100]  {pow(2,x)} node[pos=0.52, right]{$y=2^n$};
\addplot[blue, domain=0:18, samples=100]  {x} node[pos = 0.89, above left] {$y=n$};
\end{axis}
\end{tikzpicture}
\end{center}

The code below gets plotted as:

however, I would like the grey lines not to overlap the x- and y-axis, but the graph should not change otherwise - when I tried axis lines *= left, it got shifted a little bit, as can be seen here (which is something I do not want):

which is something I want to achieve partially (the axis are fixed), however the plots do not look like on the first picture (since they are shifted).

Any ideas?

Answer 1

You can use elargelimits=false or enlargelimits=upper to achieve your goal.

\documentclass{article}
\usepackage{pgfplots}
\begin{document}
  \begin{center}
\begin{tikzpicture}[scale=1, transform shape]
\begin{axis}[grid=both,
      mark = none,
      xmin = 0, ymin = 0,
      xmax = 16,ymax = 16,
      axis lines*=middle,
      enlargelimits=upper,
      clip=false,
      xtick={0,2,...,16},
      ytick={0,2,...,16}]
\addplot[red, domain=0:5,restrict y to domain=0:18, samples=100]  {pow(2,x)} node[right,anchor=north west]{$y=2^n$};
\addplot[blue, domain=0:18, samples=100]  {x} node[anchor=north east,inner xsep=3ex] {$y=n$};
\end{axis}
\end{tikzpicture}
\end{center}
\end{document}

You can dispense with pos by playing with anchors and inner sep as I did.