# Plotting several functions with TikZ/pgf

How do I plot several functions in Latex with tikz?

I want it to look something like this:

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:

And:

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?

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}


• What do I then do, if I want to plot from x=-2..2 and y=-2..2? But this plot below seems a bit odd. The red and the blue functions are supposed to touch at exactly (2,-1). – RandomDude Sep 9 '14 at 19:46
• I mistyped the function from your example. Instead of -\x / 3 + 1/5 it should be -3/5 * \x + 1/5. In any case, you can use domain = -2:2 in the parameters to \draw to restrict the values of your variables. – Derek Sep 9 '14 at 20:03

A general template with PSTricks.

\documentclass[pstricks,border=0pt,12pt,dvipsnames]{standalone}
\usepackage{amsmath}
\usepackage{pst-plot}
% \usepackage{pst-math} provides ATAN
\usepackage[nomessages]{fp}

\FPeval\XMin{0-2*pi}
\FPeval\XMax{2*pi}
\FPeval\YMin{0-pi}
\FPeval\YMax{2*pi}

\FPeval\XOL{0-1/2} % of DeltaX
\FPeval\XOR{1/2} % of DeltaX
\FPeval\YOB{0-1/5} % of DeltaY
\FPeval\YOT{1/5} % of DeltaY

\FPset\xTrigLabelBase{4}
\FPset\yTrigLabelBase{6}
\FPset\Dx{1}
\FPset\Dy{3}

\FPeval\dx{pi/xTrigLabelBase*Dx}
\FPeval\dy{pi/yTrigLabelBase*Dy}

\FPeval\AxisL{XMin+dx*XOL}
\FPeval\AxisR{XMax+dx*XOR}
\FPeval\AxisB{YMin+dy*YOB}
\FPeval\AxisT{YMax+dy*YOT}

\newlength\Width\Width=12cm
\newlength\Height\Height=8cm

\newlength\llx\llx=-5pt
\newlength\urx\urx=15pt
\newlength\lly\lly=-5pt
\newlength\ury\ury=15pt

\psset
{
llx=\llx,
lly=\lly,
urx=\urx,
ury=\ury,
xtrigLabels=true,
ytrigLabels=true,
xtrigLabelBase=\xTrigLabelBase,
ytrigLabelBase=\yTrigLabelBase,
labelFontSize=\scriptstyle,
xAxisLabel=$x$,
yAxisLabel=$y$,
algebraic,
plotpoints=500,
}

\newpsstyle{mygrid}
{
dx=\dx,
dy=\dy,
%Dx=\Dx,
%Dy=\Dy,
labels=none,
subticks=5,
tickwidth=.4pt,
subtickwidth=.2pt,
tickcolor=Red!30,
subtickcolor=ForestGreen!30,
xticksize=\YMin\space \YMax,
yticksize=\XMin\space \XMax,
subticksize=1,
}

\def\f{Pi*sin(x)}
\def\fp{Derive(1,\f)}

\def\g{2*asin(x/(2*Pi))}

\begin{document}
\pslegend[lt]{%
\color{NavyBlue}\rule{12pt}{1pt} & \color{NavyBlue} $y=\pi\sin x$ \\
\color{Red}\rule{12pt}{1pt} & \color{Red} $y=\pi\cos x$ \\
\color{ForestGreen}\rule{12pt}{1pt} & \color{ForestGreen} $y=2\sin^{-1}\left(\tfrac{x}{2\pi}\right)$
}
\begin{psgraph}
[
dx=\dx,
dy=\dy,
Dx=\Dx,
Dy=\Dy,
linecolor=gray,
tickcolor=gray,
ticksize=-3pt 3pt,
axespos=top,
]{<->}(0,0)(\AxisL,\AxisB)(\AxisR,\AxisT){\dimexpr\Width-\urx+\llx}{!}%{\dimexpr\Height-\ury+\lly}
\psaxes[style=mygrid](0,0)(\XMin,\YMin)(\XMax,\YMax)
\psplot[linecolor=NavyBlue]{\XMin}{\XMax}{\f}
\psplot[linecolor=Red]{\XMin}{\XMax}{\fp}
\psplot[linecolor=ForestGreen]{\XMin}{\XMax}{\g}
% -------------------
% tangent and normal
\psplotTangent[linecolor=Magenta]{Pi 3 div 2 mul}{1.5}{\f}
\psplotTangent[linecolor=Cyan,Derive={-1/\fp}]{Pi 3 div 2 mul}{1.5}{\f}
%
% sum
\psplot[linecolor=Rhodamine]{\XMin}{\XMax}{Sum(i,0,1,7,(-1)^(i)*x^(2*i)/fact(2*i))}
\end{psgraph}
\end{document}


• So very many keystrokes. PSTricks seems really verbose compared to the TikZ solutions posted. – Jake Sep 9 '14 at 18:19
• @cyanide-basedfood So very many keystrokes. I think he's not really comparing :) – Manuel Sep 9 '14 at 18:23
• The axes setting seems to be verbose as I have not bundled it into my own package. – kiss my armpit Sep 9 '14 at 18:25
• If you carefully read my code above, you will see there are many important things buried there. For example, I presented tangent line, sum of several functions (sinusoidal series), derivative, trigonometric axis, fractional axis, and many more. – kiss my armpit Sep 9 '14 at 18:27
• This is a good help for understanding TikZ a little better, thank you :) – RandomDude Sep 9 '14 at 19:34

It seems like the error is in the notation. You should not include the "\" just before the function square root:

\draw[color=blue] plot[domain=-5:5] function{x/2 + 1/2 - 1/2 * sqrt{5x^2+2x+1}};

On the other hand, be sure the function is defined in the domain you ask to be plotted.

• It isn't sqrt{…} but sqrt(…). – Manuel Sep 9 '14 at 17:27

If use of gunplot is preferred, this is how. Pdflatex -shell-escape is required and install of gnuplot in the system.

Code

\documentclass{article}
\usepackage{tikz}

%\pagestyle{empty}

\begin{document}
\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}

\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/3 + 0.2}  node[right] {$f(x)$};
\draw[color=blue] plot[id=a] function{x/2+0.5-sqrt(5*x**2+2*x+1)/2}
node[right] {$g(x)$};
\end{tikzpicture}
\end{document}

• How do i plot the functions from x=-2..2 and y=-2..2? And this plot below seems a bit odd. The f(x) is supposed to be a tangent line at (2,-1), so they are supposed to touch each other at exactly that point, but they don't seems to. – RandomDude Sep 9 '14 at 19:55
• OK, put domain=-2:2 right after id=x with a comma to separate them. Further, the function should have been -3*x/5+0.2. – Jesse Sep 9 '14 at 22:12