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Part 5: Graphing Functions

All of the standard mathematical functions, plus many other functions, are available in MATLAB. Functions operate both on both single numbers and on vectors. You can use MATLAB just like a calculator.

  1. Enter

    y = cos(3.5)    % Assumes radians
  2. Enter

    x = [-2, 4, 1, -1]
    z = sin(x)
  3. Enter

    w = log(1 + abs(x))./atan(x)      % Note the period

The standard method of graphing functions in MATLAB requires you to make lists (really vectors) of x values and y values and then give the command to plot the (x,y) pairs. You can get a list of x values covering the range you need by using a command of the form:
    x = xstart: xincrement: xend .
Below, we plot the built-in function y = exp(x) on the interval from Ė1 to 2.

  1. Enter
  2. x = -1: 0.1: 2
    y = exp(x)
    plot(x, y)

Usually, we donít want to print out the x and y lists so we use a semi-colon to suppress the output.

We can control the graph's color and line style by adding an extra parameter to the plot command. Choices for colors are 'c' (cyan), 'm' (magenta), 'y' (yellow), 'r' (red), 'g' (green), 'b' (blue), 'w' (white), and 'k' (black). Line style choices are '-' for solid (the default), '- -' for dashed, ':' for dotted, and '- .' for dash-dot. Let's make the graph red and dotted.

  1. Enter

  2. x = - 4: 0.5: 3;
    y = cos(x);
    plot(x, y, 'r:')

MATLAB has marker types '+', 'o', ' * ', and 'x' and the filled marker types 's' for square, 'd' for diamond, '^' for up triangle, 'v' for down triangle, '<' for right triangle, '>' for left triangle, 'p' for pentagram, and 'h' for hexagram. If you specify a marker but not a line style, your graph only has disconnected markers. Here we plot blue diamonds.

  1. Enter

    plot(x, y, 'bd')

Using unconnected markers is just what we want in order to produce a scatter-plot of data points. Rarely do we want such points connected by lines.

  1. Enter
  2. x = [1, 2, 4, 5, 7]
    y = [10, - 4, 3, 1, 6]
    plot(x, y, 'ro')

We can plot more than one graph on a single plot by using the hold on command to save the old plot and then make another plot the usual way. Below, we add the line y = - 3*x + 15 to the last scatter-plot.

  1. Enter

  2. hold on
    x = 1: 0.2: 7;
    y = - 3*x + 15;
    plot(x, y, 'b')

There are additional commands that allow us to control the "window" of the graph, add grid lines, put labels on the axes, add a title for the graph, and specify a legend. We will add these features to our plot.

  1. Enter

  2. % Window: 1 < x < 7, - 5 < y < 1
    axis( [1, 7, - 5, 11] )
    grid on
    xlabel( 'x values' )
    ylabel( 'y-axis' )
    title( 'Plot of y versus x' )
    legend( 'data points', 'line')

There is another, sometimes easier, way to make a plot in MATLAB; using the fplot function. You simply put the name of your function in single quotes. You can use line markers for the curve like '- +', '- x', '- o', and '- *'. You have no choice of color and generally have less control over the appearance of the plot. To find out more about features of fplot, type "help fplot" at the MATLAB prompt.

  1. Enter

  2. clf    % clears figure window
    fplot('sin(x)', [- 3, 3])
    grid on

Experiment with combinations of the commands used for plotting to be sure you feel comfortable using them.

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