MATH 163, Spring 2001 Due Date: Name(s):
Extra Project 1.3a: Variations in the Graph of a Function
Objective
To illustrate the variations in the graph of a function that result from variations in the way the function
is specified.
Narrative
If you have not already done so, read Section 1.3 of the text.
In this project, we investigate the variations in the graph of the function f that result from varying the
definition of f.
Task
a) Type the command lines below into Maple in the order in which they are listed. They produce a graph
of f(x) = x3
- x.
> # Project 1.3a: Variations in the Graph of a Function
> restart; Clear Maple's memory.
> f := x -> x^3-x; Let f(x) = x3
- x.
> plot(f(x),x=-4..4,y=-6..6); Plot the graph of f over the interval [-4, 4].
b) Continue by typing the following lines into Maple.
> plot({f(x),f(x+2),f(x-2),f(x)+2,f(x)-2},x=-4..4,y=-6..6);
> plot({f(x),f(2*x),f(x/2),2*f(x),f(x)/2},x=-4..4,y=-6..6);
> plot({f(x),f(-2*x),f(-x/2),-2*f(x),-f(x)/2},x=-4..4,y=-6..6);
At this point, make a hard-copy of your typed input and Maple's responses. Then ...
c) label the curves in each of the plots you produced in part (b). For example, label the graph of f in each
plot by y = f(x). (If your hard-copy will not be in color, it might be useful to refer to the color output on
your computer monitor when doing this labeling.)