how to plot the functions in TikZ?

Question

I would like to plot a linear function as y=40-0.2x and an hyperbola as y=5/x. How could I make it? I've tried, a code from this document in p. 160, but the curve wasn't in the same page with the axes.

EDIT: Having used the Tikz method mentionned below, I would like to make a graph for y=5/(x-1)+1.

The result as it is shown in Microsoft Mathematics is:

However, using LaTeX, I don't have the same result. My code is:

\documentclass[tikz,border=3mm]{standalone}
\usepackage[english,greek]{babel}
\usepackage{ucs} 
\usepackage[utf8x]{inputenc}
\begin{document}
\begin{tikzpicture}[xscale=0.08,yscale=0.09,domain=0.140:60,samples=800]
    \draw[->] (0,0) -- (65,0) node[below] {$x$};
    \draw[->] (0,0) -- (0,35) node[left] {$y$};
    \foreach \i in {10,20,...,50} {
        \draw (\i,1) -- (\i,-1) node[below] {$\i$};
    }
    \foreach \i in {5,10,...,30} {
        \draw (1,\i) -- (-1,\i) node[left] {$\i$};
    }
    \draw[green] plot (\x,{5/(\x-1)+1});
\end{tikzpicture}
\end{document}

Where is my fault?

Answer 1

Remarks

Keep in mind for both methods, that 5/x has a singularity at 0. At this point the function value will be infinity, which is kind of hard to draw for PGF and will therefore throw an error:

• ! Package PGF Math Error: You've asked me to divide `5' by `0', but I cannot divide any number by `0' (in '{5/0}').

• ? Dimensions too large

Method 1: Using TikZ

The advantage of using TikZ here is, that you can easily place nodes on the plot. The disadvantage is, that you have to scale x and y dimension, because else the drawing will be 220cm wide.

Implementation

\documentclass[tikz,border=3mm]{standalone}
\begin{document}
\begin{tikzpicture}[xscale=0.04,yscale=0.08,domain=0.125:220,samples=400]
    \draw[->] (-10,0) -- (225,0) node[below] {$x$};
    \draw[->] (0,-5) -- (0,45) node[left] {$y$};
    \foreach \i in {50,100,...,200} {
        \draw (\i,1) -- (\i,-1) node[below] {$\i$};
    }
    \foreach \i in {10,20,...,40} {
        \draw (1,\i) -- (-1,\i) node[left] {$\i$};
    }
    \draw[blue] plot (\x,{40-0.2*\x});
    \draw[red] plot (\x,{5/\x});
\end{tikzpicture}
\end{document}

Output

Method 2: Using PGFPlots

This is much more elegant and the code is much shorter.

Implementation

\documentclass[tikz,border=3mm]{standalone}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
    \begin{axis}[domain=0.125:220,samples=400]
        \addplot+[mark=none] {40-0.2*x};
        \addplot+[mark=none] {5/x};
    \end{axis}
\end{tikzpicture}

\begin{tikzpicture}
    \begin{axis}[
        domain=0.125:220,
        xmin=-10, xmax=220,
        ymin=-5, ymax=45,
        samples=400,
        axis y line=center,
        axis x line=middle,
    ]
        \addplot+[mark=none] {40-0.2*x};
        \addplot+[mark=none] {5/x};
    \end{axis}
\end{tikzpicture}
\end{document}

Output

Method 3: PSTricks (Just for fun)

Using the package pst-plot you get access to advanced plotting features. Also PSTricks is much faster than TikZ for plotting, because it makes use of the Postscript language.

Implementation

Compile with xelatex or latex -> dvips -> ps2pdf.

\documentclass[pstricks,border=3mm]{standalone}
\usepackage{pst-plot}
\begin{document}
\begin{pspicture}[xAxisLabel=$x$,yAxisLabel=$y$](-0.5,0)(0.5,6.5)
\begin{psgraph}[arrows=->,Dx=50,Dy=10](0,0)(-10,-5)(220,45){8cm}{6cm}
    \psplot[plotpoints=200,linecolor=blue]{0}{220}{40 0.2 x mul sub}
    \psplot[plotpoints=200,linecolor=red]{0.125}{220}{5 x div}
\end{psgraph}
\end{pspicture}

\begin{pspicture}[xAxisLabel=$x$,yAxisLabel=$y$,xAxisLabelPos={c,-12},yAxisLabelPos={-35,c}](-1,-1)(0.5,6.5)
\begin{psgraph}[axesstyle=frame,xticksize=-5 45,yticksize=-10 220,Dx=50,Dy=10](0,0)(-10,-5)(220,45){8cm}{6cm}
    \psplot[plotpoints=200,linecolor=blue]{0}{220}{40 0.2 x mul sub}
    \psplot[plotpoints=200,linecolor=red]{0.125}{220}{5 x div}
\end{psgraph}
\end{pspicture}
\end{document}

Answer 2

Answer to the edit

You need to adjust the plot limits by hand. There is no way around that, because no plotting software in the world can know, what limits you want.

Implementation

\documentclass[tikz,border=3mm]{standalone}
\usepackage[english,greek]{babel}
\usepackage[utf8]{inputenc}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}[xscale=1.5,yscale=0.04,domain=1.037:4,samples=800]
    \draw[->] (0,0) -- (4.5,0) node[below] {$x$};
    \draw[->] (0,0) -- (0,135) node[left] {$y$};
    \foreach \i in {1,2,...,4} {
        \draw (\i,1) -- (\i,-1) node[below] {$\i$};
    }
    \foreach \i in {20,40,...,130} {
        \draw (0.05,\i) -- (-0.05,\i) node[left] {$\i$};
    }

    \draw[green] plot (\x,{5/(\x-1)+1});
\end{tikzpicture}

\begin{tikzpicture}
    \begin{axis}[
        domain=1.037:4,
        xmin=0, xmax=4.5,
        ymin=0, ymax=135,
        samples=800,
        axis lines=center,
    ]
        \addplot+[mark=none,color=green] {5/(x-1)+1};
    \end{axis}
\end{tikzpicture}
\end{document}

Output

Answer 3

Just for fun with PSTricks.

\documentclass[preview,border=12mm,varwidth]{standalone}
\usepackage{pst-plot}

\psset{plotpoints=200,linewidth=1pt,algebraic,xAxisLabel=$x$,yAxisLabel=$y$}

\def\f{40-0.2*x}
\def\g{5/x}

\begin{document}

\begin{psgraph}[arrows=->,Dx=50,Dy=10](0,0)(-10,-5)(220,45){8cm}{6cm}
    \psplot[linecolor=blue]{0}{220}{\f}
    \psplot[linecolor=red]{0.125}{220}{\g}
\end{psgraph}

\vspace{1cm}
\psset{xAxisLabelPos={c,-12},yAxisLabelPos={-35,c}}
\begin{psgraph}[axesstyle=frame,xticksize=-5 45,yticksize=-10 220,Dx=50,Dy=10](0,0)(-10,-5)(220,45){8cm}{6cm}
    \psplot[linecolor=blue]{0}{220}{\f}
    \psplot[linecolor=red]{0.125}{220}{\g}
\end{psgraph}

\end{document}