[Tex/LaTex] Plotting several functions with TikZ/pgf

pgfplotstikz-pgf

How do I plot several functions in Latex with tikz?

I want it to look something like this:

enter image description here

With the this code:

\documentclass{article}

\usepackage[latin1]{inputenc}
\usepackage{tikz}

% GNUPLOT required
\begin{document}
\pagestyle{empty}


\begin{tikzpicture}[domain=0:4]
\draw[very thin,color=gray] (-0.1,-1.1) grid (3.9,3.9);
\draw[->] (-0.2,0) -- (4.2,0) node[right] {$x$};
\draw[->] (0,-1.2) -- (0,4.2) node[above] {$f(x)$};
\draw[color=red] plot[id=x] function{x} 
    node[right] {$f(x) =x$};
\draw[color=blue] plot[id=sin] function{sin(x)} 
    node[right] {$f(x) = \sin x$};
\draw[color=orange] plot[id=exp] function{0.05*exp(x)} 
    node[right] {$f(x) = \frac{1}{20} \mathrm e^x$};
\end{tikzpicture}


\end{document}

This does actually work.

But as soon as I insert a little bit more complicated functions like:

enter image description here

And:

enter image description here

It simply fails, and gives me an error:

\begin{tikzpicture}[domain=0:4]
\draw[very thin,color=gray] (-0.1,-1.1) grid (3.9,3.9);
\draw[->] (-0.2,0) -- (4.2,0) node[right] {$x$};
\draw[->] (0,-1.2) -- (0,4.2) node[above] {$f(x)$};
\draw[color=red] plot[id=x] function{-1/3x+1/5} 
    node[right] {$f(x) =x$};
\draw[color=blue] plot[id=sin] function{1/2x+1/2-1/2\sqrt{5x^2+2x+1}} 
    node[right] {$f(x) = \sin x$};
\end{tikzpicture}

How do I solve this?

Best Answer

As Efraín Soto A. pointed out, "sqrt" shouldn't have a leading backslash. I just want to point out that you can do this with straight tikz/pgf --- GNUPLOT isn't necessary:

\documentclass{article}

\usepackage[latin1]{inputenc}
\usepackage{tikz}

\begin{document}
\pagestyle{empty}

\begin{tikzpicture}[domain=0:4]
  \draw[very thin,color=gray] (-0.1,-1.1) grid (3.9,3.9);
  \draw[->] (-0.2,0) -- (4.2,0) node[right] {$x$};
  \draw[->] (0,-1.2) -- (0,4.2) node[above] {$f(x)$};
  \draw[color=red] plot (\x, \x) node[right] {$f(x) =x$};
  \draw[color=blue] plot (\x, { sin(\x r) }) node[right] {$f(x) = \sin x$};
  \draw[color=orange] plot (\x, { 0.05*exp(\x) })
    node[right] {$f(x) = \frac{1}{20} \mathrm e^{x}$};
\end{tikzpicture}

\begin{tikzpicture}[domain=0:4]
  \draw[very thin,color=gray] (-0.1,-1.1) grid (3.9,3.9);
  \draw[->] (-0.2,0) -- (4.2,0) node[right] {$x$};
  \draw[->] (0,-1.2) -- (0,4.2) node[above] {$f(x)$};
  \draw[color=red] plot (\x, {-\x / 3 + 1/5}) node[right] {$f(x)$};
  \draw[color=blue] plot
    (\x, { 1/2 * \x + 1/2 - 1/2 * sqrt(5 * \x^2 + 2*\x + 1)})
    node[right] {$g(x)$};
\end{tikzpicture}

\end{document}

The plot.

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