Plotting Functions for Kids (and Adults) on an Apple Computer plot functions for free!

To plot functions on the computer, you need to install a program called gnuplot. See the section below called Installing gnuplot for how to do that.

To start gnuplot you first have to open the Terminal program on your Mac. You will be able to type into that window. You should type gnuplot and press Return. Then you’ll see:

	G N U P L O T
	Version 5.2 patchlevel 6    last modified 2019-01-01

	Copyright (C) 1986-1993, 1998, 2004, 2007-2018
	Thomas Williams, Colin Kelley and many others

	gnuplot home:     http://www.gnuplot.info
	faq, bugs, etc:   type "help FAQ"
	immediate help:   type "help"  (plot window: hit 'h')

Terminal type is now 'qt'
gnuplot>

Now you need to do a few things to set up the plot. To turn on grid lines, type set grid and press Return. It will look like:

gnuplot> set grid
gnuplot>

Next you need to define your functions. Their names can be anything you want and they are what will appear in the legend, so chose something that makes sense (it is possible to change the legend, but it is easier to let gnuplot chose it for you. For example, we will use the names noshrink and mighty from a recent math homework. Formulae in gnuplot are not represented with x and y, but with f(x) and x, where f(x) is just like y and the f part can be any name. This will look like:

gnuplot> noshrink(x) = 4.5 * x
gnuplot> mighty(x) = x + 45
gnuplot>

and this is the same as \(y = 4.5 \times x\) for noshrink and \(y = x + 45\) for mighty.

At this point, you have done three things:

1. Turned on the grid in your plot
2. Defined the formula for noshrink
3. Defined the formula for mighty

You can define as few as one formula or as many as you want.

To plot your formulae and see them on the screen, you need to know what the range of x values are that you want to use. In the example below we have chosen a range from 0 to 60 by typing x=[0:60] as part of the plot command:

gnuplot> plot [x=0:60] noshrink(x), mighty(x)
gnuplot>

and you will see a window pop up on the screen that looks like the picture in Figure 1.

If the plot looks right, you can save it to a PDF file for printing or emailing. Saving a plot to a PDF is a few more steps that you have to type at the gnuplot> prompt. You need to set the output type (PDF) and the name of the output file and then make the plot again and finally set the output back to the screen:

gnuplot> set term pdf

Terminal type is now 'pdfcairo'
Options are ' transparent enhanced fontscale 0.5 size 5.00in, 3.00in '
gnuplot> set output "my-plot.pdf"
gnuplot> replot
gnuplot> unset term

Terminal type is now 'qt'
gnuplot>

You can change the name of the file from my-plot.pdf to anything you want; it’s best to end it with .pdf though. You can open the PDF file with Preview and print it if you want. To open the file in Preview without exiting gnuplot you can type ! open my-plot.pdf (or whatever the name of your files is) at the gnuplot> prompt, like:

gnuplot> !open my-plot.pdf
gnuplot>

and Preview will open and show you your file.

When you’re done, you can exit gnuplot by typing exit and pressing Return.