# Plotting Functions

## Basic Plots Commands

• Plotting functions is one of the easiest functions of the Maple program. However, there are a couple of important syntax rules that you must follow. First of all, the general form is

plot(expression, x = a..b, other options);

So, let's try and example. We want to plot ; from to Note how we write as x^2. The correct command is

> plot(x^2,x=-4..4);

Exercise: Now try to plot y = x^3; from x = -2; to x = 3.

• Sometimes it useful to plot a mathematical expression on which you are doing other things. For this purpose we define an expression as follows:

f := any mathematical expression

Here are some examples: Note the power notation. In Maple we write

3^2 for .

 f := 1+2*(x-3)^2 Mathematically this expression is g: = (x+1)/(x^3-2) Mathematically this expression is

Example. Plot f := , from . to Execute the commands

>f := 1+2*(x-3)^2; Note the semicolon after each statement.

>plot(f,x=-1..2);

• Next we include the (vertical) range for the plot. If we wish to plot the previous expression for f between and displaying the the vertical range from to we first define the expression and then include the range as the third argument'' of the plot command as follows. Note the commas between arguments of the plot command. Note the semicolon after each and every Maple statement.

> plot(f,x=-4..4, -4..10);

Exercise: Now try to plot the expression representing the function from to with the range to

## Plotting Parametric Functions

It is important and easy to plot parametric equations. The basic form is

of the calling sequence is

 >plot(\lbrack x(t),y(t),t=range of t\rbrack,h,v,options);

where h = horizontal range, v = vertical range, and other options. For example the parametric equations of the parabola

To plot these parametric equations from to execute the command

>plot(\lbrack t,t^2,  t=-1..2\rbrack );

Other examples of plot parametric commands are

> plot(\lbrack sin(t),cos(t),t=0..Pi\rbrack);

> plot(\lbrack x^2,x,x=0..3*Pi\rbrack,-8..8,-10..10);

> plot( \lbrack(t^2-1)/(t^2+1),2*t/(t^2+1), t=-infinity..infinity\rbrack );

In the third example above, the range of is

Exercise Plot the parametric equations and for to You should get the following graph.

Exercises

1. Plot the function from to Plot the function from to with range from to 4.

2. Use the help manual to plot the function from to with plot thickness

3. Use and expression for and plot it from to 5.

4. Plot the parametric equation for to

5. Plot the parametric equation for to (Hint. The absolute value function has the Maple syntax: abs(t).)

This document created by Scientific Notebook 4.0.